If you're prepping for multiplayer, my recommendation is 1v1 against a hard difficulty AI.  Don't just aim to win, aim to mop the floor with it.  Everything above "normal" isn't more intelligent, it just gets a resource cheat.  This makes "hard" nice to practice against, since its resource cheat is just enough to cover for its inept resource management.  Any higher on the difficulty scale and you're really just learning how to beat an excessive number of poorly managed units.  That's a challenge in and of itself, but not directly applicable to multiplayer.

Use standard multiplayer settings if you're practicing for multiplayer: all speeds set to fastest, normal fleet size, pirates off, locked teams, diplomatic victory off.

I'd say these are the most important skills you need to pick up before hitting multiplayer:

1. Fast Expansion:  Quickly and efficiently setting up your empire is huge in this game.  You need to be able to expand quickly in multiple directions.  This means being able to use small forces of frigates to take down militia without any capital ship support (enabling your capital ship to take down tougher militia).  You should be able to colonize an asteroid with only a colony frigate (hint: colonize the roid then quickly build a turret...)
2. Know the Units:  You should have a general idea of what every unit does, what it's good at, and what it's bad at.  At very least know the carrier-class capital ships, the long-range frigates, the support cruisers, and the starbases.
3. Minimalism:  Know how to get maximum bang for your buck.  This applies both to developing your economy and your fleet.  This means having a general sense of timing when it comes to teching, increasing fleet size, and growing your economy.  You don't need to perfect, you just need to have a general sense. 

Two things to watch out for with human opponents.  First of all, they'll go around your static defenses, making turrets, and even starbases ineffective.  Hangers are unfortunately quite overpriced, so your best defense is actually the repair platform, since you can run injured units back into its effect.  Put a frigate factory into the mix to produce reinforcements on site and you have a cheap and effective early-game defense.  The second issue to watch for is that they don't play predictably, and may jump past several neutral planets to grab a staging post next to your empire.  You need to be scouting carefully for this, because if a human opponent puts up three frigate factories and starts pumping units in close proximity that early, it can be very difficult to survive.

Beyond that, my only piece of advice is to try to downplay the amount of tech your research.  Tech is important, but early-game I find most beginners get way too much of it.  If it's slowing down your expansion or compromising your fleet, you're buying too much tech.  Most technology performs better for larger empires with bigger fleets and bigger economies, so it doesn't make much sense for your early-game empire with 3 planets and 20 frigates.

thanks for the advice. I'm going to start a match right now. Maybe I'll see you online.

Before coming online (for pvp and not comp stomps) you want to be comfortable with all of the basic game mechanics.  You should know how to do everything you might want to do such as capturing neutral extractors or managing ships in combat or being able to set them so that they won't automatically attack enemy ships on the other side of the gravity well.  You need to know your units like Darvin said (see Raging Amish's unit discussion guide sticky post in the Strategy forum).  Also, you need to be familiar with all three races and know their strengths and weaknesses.  Then you'll be in a good position to come online and start learning the people v. people game.

I joined as WhippersnapperUT99.  Fortunately I had an old Half-Life collection CD I was able to use to activate Steam.