I know that most people on here are only really interested in online play, and fair enough. But me - I'm a sins comp-stomper. I play my fps games online, but with sins I prefer to play the AI and stack the odds against me. I like the challenge of beating back constant attack by an enemy with massive numerical superiority. "Never underestimate the power of stupid things in large numbers".
Anyway, this is just a quick collection of tips for playing against the AI when heavily outnumbered (probably with multiple hard AIs teamed against you). It assumes you are playing as TEC but most is transferrable. The defenses of entrenchment completely alter the balance of power in these scenarios compared to vanilla sins, so lets explore them 
The start (same as vanilla sins):
The most important thing for the start is to get your empire frontiers established quickly. Build a few scouts and set them exploring. Decide beforehand how far you are going to go in claiming neutral planets. *Do not push too far!* In early-mid game (the toughest part) it's easier to defend a smaller well-connected territory than it is to defend a larger one, even with the larger economy the large one brings. You ideally want a small number of closely-grouped worlds with the fewest number of entry points. Asteroids are much easier to defend than planets, so if you can use one of these as a choke-point then go for it.
One you have picked your planets, go capture them ASAP. If you feel you can get away with it, a colony cap-ship is the way to go, but I usually end up going for the kol instead, because it's so durable that I can use it as a damage soak throughout the early game. Once you have a planet, get a few (~5) gauss turrets up as soon as possible.
As far as building, the first thing you want is a few light frigates (4 will capture an asteroid without loss). When you go to capture a neutral planet, jump the cap ship in a couple of seconds earlier and it will draw most of the fire. After this, you will want two civic research stations, since you need to get trade research performed quickly, and also may need volcanic / arctic exploitation research. If you can build 3 trade ports quickly, that will give a nice boost to your early-game credit income.
Mantra for the early game: Take only what you can hold, but hold whatever you take.
Mid-game (early):
This usually covers say 30 - 90mins game time, in a large map against multiple AIs. The point here is survival. I'm always tempted to push more effort into building up my economy, but every time I do I get crushed. You need to focus on defense. Get 15 gauss turrets in each frontline planet ASAP (this will slow down the typical early enemy fleet well enough for you to replace your losses). Ideally you want to build enough in the way of defenses that the enemy hold back their attack. If they attack and you constantly have to replace turrets / ships, then your overstretched economy may completely stall, and you will go under.
Once you have the enemy temporarily held at bay, it's time to solidify those positions. Go for starbase research as soon as possible (3 military stations required). Once you have a starbase and 15+ gauss turrets you will be okay. One point though - as soon as you drop a starbase in a frontline location, IMMEDIATELY upgrade its structural integrity by one point. A basic starbase is just a sitting duck, but with one upgrade it becomes a lot more durable. Other upgrades can be done as the enemy fleet enters, but always go for structural integrity first. You can upgrade the weapons once the battle is in full swing, but weapons aren't much use if the base is just debris.
At this stage, I find a small fleet of one kol and a few LRMs are quite effective. When the enemy attacks, jump in with your kol, move near to the static defenses, and try to draw their fire. If some of them do target the kol, you can take some damage and then withdraw it, splitting the fleet and lightening the load on your defenses.
Mid-game (later):
So your empire is protected from the constant onslaught by a couple of starbases and a cubic assload of gauss turrets. Now you can really focus on your economy. As I said earlier, it's tempting to try and skip forwards to this phase, but depending on just how outnumbered you are it might not be possible.
Anyway, with TEC this means two things: Trade ports and pervasive economy. Against a large number of enemies, pervasive economy is essential, and will provide you masses of credits. So, find room somewhere for 6 civic research stations, and get development mandate research done. Then place two more civic labs and work towards PE. Other than this, place as many trade ports as your planets will allow. Always place a trade port on dead asteroids, to help maintain trade routes. If you only have a few planets and space is at a premium, then place star bases on your inner worlds also, and fill them with trade and ship construction upgrades. Go for the black market price reduction research option early too, as the mass of credits will mean you're buying from the black market frequently.
Here you will want to build up your fleet. I try to hold off building an offensive fleet until my economy is close to complete. As soon as you start working through the fleet supply ranks your income takes a nosedive, so try to stick to just one or two research jumps (<400 FS) until your economy is in shape.
During this phase don't forget defense, or you will pay the price with 3-fleet co-ordinated attacks coming your way. Upgrade your starbases (structural first, then hanger, then weapons when the enemy jumps in). Max out your tactical slots with repair bays and gauss turrets. Research mines, and if you have enough cash or metal, then start laying them (see later for more on mines).
Late game:
Finally, when you have a fleet, you will be able to break out. Everyone has their own ideas for fleet formation, but against the AI I find that a mixture of capital ships, a lot of heavy cruisers, and "enough" support carriers works extremely well. The kodiaks dish out and soak up a lot of damage, the carriers provide a fighter screen, and the caps pin the fleet together. Again, I always jump in with my caps a few seconds earlier than the rest of the fleet (helps with mine clearing, and with the enemy targeting your capships first, which you can usually withdraw rather than losing).
The key tactic here is to attack the correct worlds. Attack by prefence a world which will act as a new choke point, cutting off a large section of enemy territory. You can then sit in this new position, heavily defend it (starport + gause + maybe mines). Once it is fortified you can work your way through the cut-off territory at will. This is the key basic tactic in entrenchment, and is only possible with the new defenses. It makes capturing territory a lot more methodical than in sins, where you could expect almost constant counter-attacks to newly captured worlds.
As well as an attack fleet, you will need a defense force. Your starbase and gauss turrets are powerful, but no match for a 3-enemy simultaneous attack with over 1000 fleet supply each. I have found that by far the best ship for the job is the Kol, backed with support carriers. I tried using kodiaks, but 4 kols seem to do the job better than 50+ kodiaks. Basically, the job of the defensive fleet is to draw as much fire as possible away from the static defenses, and if possible to split up the enemy fleet. The starbase and gauss turrets will dish out enough damage that you don't need to worry about dealing it out with your defense fleet. As in early game, the best tactic is to get stuck right into the enemy fleet as it's attacking your starbase position. If a large portion of the fleet is attacking one of your ships, withdraw to the edge of the well and see if that fleet will follow you. Also, keep replacing destroyed gauss turrets until all the constructor ships are gone. Try to place new turrets behind the older ones, to avid the construction ships being directly in the line of fire.
For the defense fleet, I try to have around 20 light carriers. Always build fighters - you just want to protect against bombers, the starbase will do the actual damage. The 14 fighter squads from the SB, the 40 from the carriers, and the ~10 from the kols should keep the enemy bomber number down to a minimum. I tried flak frigates, but they need to get into the thick of it to be effective and just don't last more than a few seconds. I might keep 4 or 5 kodiaks back in the next grav well, to jump in and go for any seige frigates which are navigated around the defenses.
In general:
Remember, when you have multiple enemies teamed against you, the only way to win out in the end is to out-economy them. For this, you will first need to destroy their ships a lot more efficiently than than they can destroy your defenses. Ie if they attack with a fleet worth 50,000 credits total, and do only 10,000 credits damage, then you're on the right path. Equal losses are not acceptable - at least not in defense. Pervasive economy is your friend (as TEC).
Don't over-stretch your economy. Playing with a smaller fleet and replacing losses is sometimes more effective than pushing up the fleet supply and being unable to replace what you have lost.
** CAPITAL SHIPS **
The TEC don't have the fleet-busting abilities of advent capitals, but they have a soild set of capitals to choose from. TEC capitals work best against the AI in groups of 4+ with a good supporting fleet. In entrenchment it's a little easier to level up cap ships, particularly if they're on defensive duty, as entire enemy fleets can be wiped out when attacking a well defended planet. Anyway, lets take a look at the options:
Kol battleship:
This is the most durable ship in the game. It has great armour and good shields / hull, but its real power comes from the adaptive shielding ability. This will block up to 35% of all damage even when shields are down, and will block 65% of all phase missile damage. At about level 5+ you're going to have enough antimatter to keep adaptive shielding active all the time, so a high level kol is very difficult to take out. At level 6+ you will get finest hour, which again can be almost kept active constantly. This further improves the defensive capabilities of the ship.
The kol also has the flak burst ability, which at high level can be quite damaging to strike craft. You can't rely on flak burst to make too much impact on an enemy strike wing, but if used effectively early in the air battle it can tip a close air battle your way. The final ability is the gauss gun. In my eyes this is a bit of an underpowered weapon for the antimatter it costs. That said, it can be a useful ability to have if you choose the kol as your starter capital - helping it clear neutral planets more quickly.
The kol does not deal out a huge amount of damage overall - it's really a defensive ship. I like to have 1 in every large capital fleet (6+ ships), as the kol will usually move in a little in front of the other capital ships and draw the bulk of the initial fire. Combined with the shield recharge of the dunov it can be an unstoppable tank, particularly against the vasari. If you want the enemy firing at any one of your ships, it's your kol.
Dunov battlecruiser:
Not particularly well armoured or otherwise defended, and not dealing out a lot of damage, you will build a dunov for its abilities only:
Shield recharge is the main ability you will want. A couple of dunovs in a capital fleet will seriously improve its durability, since it doesn't take too much antimatter, and can recharge quite a lot of shield points. The other ability of note is 'magnetise', which will cause enemy strike craft to go crashing into the target capital ship. Of similar effectiveness to the kol's flak-burst ability, it can help turn the ide of a close air war. Use it early on in the battle when enemy strike craft are at full strength in order the maximise the amount of damage you do.
The EMP charge can be useful against an advent fleet, for draining antimatter, but for the most part I leave that ability until last. At level six the dunov gets the 'flux field' ability, which greatly reduces antimatter cost for the rest of your fleet. This is an excellent ability to have, so a high level dunov is a very valuable ship to have.
I always like to keep at least 2 dunovs in a fleet. They're better deployed in pairs so they can restore each others shields. Try to keep them towards the back of the fleet - they are not so tough as other capitals, and can't repair their own shields. If you can spare the numbers, 4 kol + 2 dunov + ~20 light carriers make a fantastic defensive fleet.
Akken battlecruiser:
This is the TECs colony cruiser. Has good abilities, but isn't so tough. The obvious ability is 'colonise', but higher levels of this just give you a free extractor. This can save time when colonising planets, but isn't worth wasting ability points on IMO. The other 'normal' abilities are 'ion bolt' and 'targeting uplink'. Ion bolt is great to have in a fleet, as it disables a ship for a few seconds. This is great for persuing fleeing capital ships, as it gives your fleet time to catch up and cause damage. Targeting uplink improves the range and fire effectiveness of nearby ships, and is a great ability to have in a close fleet. I would choose to upgrade targeting uplink first as a priority, and then ion bolt (keeping colonise at one point).
The level 6 ability is 'armistice', which stops all craft in the area fighting for a while. If you can spot an enemy fleet on approach, you can send the akkan in to weaken them, but if you're already engaged in battle beware using it. Not too effective in a defensive battle either, unless you can use it out of range of your starbase.
I always have at least 1 akkan in every fleet. If you can get away with it in early game, this is the best choice of first ship. Colonise saves money on colony frigates, and later on TU will help with the range and damage of your LRM frigates. Also, ion bolt can help you get that early critical kill on the attacking enemy capital ship. That said, sometimes it's more important to capture neutrals quickly and establish solid defensive frontiers. In this case, you should go for the kol instead.
Sova carrier:
Not as good a carrier as the advent halcyon, but still a good ship. Obviously the main reason to build one is the (up to) 6 squadrens they hold. As far as abilities go, I really like their missile platform ability, and go for this first. For some reason, enemy heavy cruisers like to target these missile platforms, which is fine by me - let them waste their precious fire! Obviously the heavy strike craft option helps a little in the air war, but the level six ability is the real winner - rapid manufacturing instantly builds strike craft, which can help a lot especially now that combat SC build rate is severely reduced. It can really win an air war.
I hardly ever use embargo. In MP I hear it's used a lot, but against massed AI hordes it isn't very effective. Frontier worlds will be heavily fortified, and a single sova won't last long, and really won't steal all that much.
Marza deadnaught:
This is the TECs assault ship. It causes the most damage of the five, but isn't so durable. The 'radiation bomb' and 'incendiary shells' abilities improve damage, but aren't particularly game changing. The raze planet ability can be useful, but usually you'll be attacking a planet with several capital ships, so I'm rarely worried about planet bombing damage rate. The level six ability 'missile barrage' can cause great damage to a fleet of lighter frigates, which would be great for early game. Unfortunately by the time it has reached level 6 that window of opportunity will usually have passed.
I rarely build the marza. It could be useful if you have to clear neutrals really quickly, but then you would usually want a 'damage soak' ship aferwards, which the marza is not.
Okay, so, what should you build? I'm going to give a breakdown for an offensive fleet of sizes 4, 8 and 12:
4 cap ships: 1 akkan, 1 kol, 2 dunov
8 cap ships: 1 akkan, 1 kol, 3 dunov, 3 sova
12 cap ships: 2 akkan, 1 kol, 4 dunov, 5 sova
Obviously each one of these should be supported by a good fleet, including heavy cruisers, support carriers with enough fighters. Flak, support cruisers and repair cruisers can also be a useful edition in smaller numbers.
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I will edit this post later to include specific information on:
* Use and placement of starbases
* Use of mines
I'll also try to include a few screenshots to better illustrate what I'm saying.