Can't grasp it

Watch the replays to see what the AI is doing. Try playing with locked teams.

I personally go for a heavy civ research start with lotsa defense and only as few ships as needed to keep the enemy at bay. This works for me 'cause I also make sure to do all the resource missions the AI sends and thus the AI either doesn't see me as a threat (The fools!) or is allied with me. I can usually keep at the second fleet supply upgrade (Relying mostly on caps in the meantime so they can level up) for up to several hours into a game if it all goes well.

Eventually I end up with the best economy and research (Both military and civilian) and then I upgrade fleet supply to the max, and proceed to rampage about.

Are you doing all of their missions? Like Kitkun points out, early on they give you resource missions to do, which aren't always easy (especially when they ask for 200 crystal), but well worth it. You can usually get 2 missions before having to fight any AIs at all, which means if you're a litle lucky you can score cease fires with 2 or so of the AIs. I actually curb my exploration early on so that I don't get too many missions at once (AIs only give missions once you've "met" them by seeing any of their ships, including scouts).

Above all, I try to make sure to ally with one of the AIs beside me, so I can leave that border undefended for a long while before worrying about it. The AI also always needs someone to fight, so if they have a cease fire or alliance with you, that means they'll go bother some other AI, who will in turn be too busy with them to attack you with a big fleet.

I know I am still pretty new to this game and I am still learning a lot but I thought that capturing planets is essential to building a strong economy. How else do you get credits, metal, and crystal?

I realize that there is a difference between exploration and capturing planets but the two go hand in hand.

I guess, I am still trying to find a balance point between how much to capture/colonize in order to support your fleets, research, and defense without spreading your fleets too thin.

Yep. Basically, don't overextend your forces. Expand to fast, and you leave yourself open to attack.

If you're good at defense and diplomacy, then you can survive long enough to build an entire fleet and do tons of research with almost no planets.

You misunderstand a little, I think I always scout the surrounding area, but once I find 4-5 planets I know I'm going to colonize, I stop my scouts from auto-exploring so they don't wander off to the other side of the map. I keep them on manual from that point on, to find choke points and scout the AIs directly next to me.

OK, that makes a more sense. The question that I have is: do you find that having colonized 4 or 5 planets is enough to sustain your economy, allow reasonable rate of research, and support a fleet (assuming that the planet population on all planets has been upgraded to allow for the most taxes)?

I have never been able to figure out how much to colonize and have always gone with "as much as posible". Of course, I've only played easy and normal AI so far.

After 4-5 planets I stop expanding aggressively, unless I need to. I play a lot of random maps, and sometimes my starting position isn't in a very optimal spot, but there's a nice choke point - then I'll take it.

The problem with grabbing too many planets too early is that they take quite a bit of an investment of resources to upgrade until they actually start churning out a decent amount of money, and it takes a while for their population to grow even then. That's why I generally pause there and start cranking out ships.

A positive side effect of not getting too many ships too early, and not scouting out some/most of the AIs - the first pirate bid you usually don't have to spend any credits on, because the AIs will bicker among themselves

Once I have 35-40 ships, I'm more confident about venturing out and being aggressive. By about that time, the AI also tends to give the first "destroy something" mission, and depending on which AI gives what, that determined my first conquest target. But I always try to get cease fires with AIs around me, so they keep the enemies busy.

Edit: What Annatar said, only not as well written.

A massive economy is quite viable against the AI, though. It's quite something to jump a bounty from 0 to 200,000 in one go.

It sounds like you need to downgrade your games a while until your ready. If you get all aggressive hard AI's, it wont be easy. Start with locked teams and let the AI's fight amongst themselves. 

I'm not sure why the 10 team diplomasy thing was ever included in the game, and unless you like chaos and being ganged up on, I think its better to turn it off.

The games back plot says all 3 are enemies, so thats how I play it. Within a race, they are freindly to each other, not possible enemies. So if I have 3 vasari, then they are a single team. They will fight me (TEC) and the Advent team. Makes life a bit more simple.

In other words apricot stacks the game slightly in his favor before starting it.

Thanks for all of the advice.  You know I played against normal to the point where it wasn't a challenge, and then jumped to hard and was overwhelmed, but I wasn't playing the diplomacy game, so I'll give that a try.  I didn't think doing the give resources missions influenced them not to attack.

I think I'll try out locked teams for a while.

Thanks again, this is a very helpful forum!

Well, just doing the one won't give you a cease fire. The first mission gives you 25% happiness, but you need 35% for a cease fire. That's why it's very important to do the first one, because most often it's the only "freebie" you get. Most others will require you to go and kill something.

I usually get two resource missions if I do the first as soon as it pops up.

You must be lucky, then