Warhawk is perfect for a quick online frag session -- if it moves, shoot it! Instant action.
The tutorials teach you the basics: First you learn to run around shooting things. (Or knifing things, at close range.) Then you learn to drive around shooting things. Finally they show you how to fly around shooting things. The basics are simple, and you start out pitted online against other noobs, so you can learn before you're completely pwned.
Once you get the hang of it, you'll find that it's fun to specialize in certain tactics. I like picking planes out of the sky with a rocket launcher. Some folks are really good with a sniper rifle. The tanks are especially fun. And I like flying, as long as there aren't too many missile launchers around.
Now that it's a Greatest Hit, it's only twenty bucks. I recommend the downloadable version.