Everything on drums is based on the single stroke roll - right-left-right-left... that is the basis of all drumming.
Assuming you're right handed, practice that roll with your kick with your right hand. Play along with recordings, television... try to play it with songs to keep it musical and not a sporting event!
When you play your kick, hold the beater against the head when you hit it. So you actually start with the beater against the head each time. This will help you immeasurably with getting a solid feel. If you're feet aren't solid, you're hands don't have a chance.
Don't try to play fast (ya right!)... it will only come with time.
Put an old pair of sticks under the seat of your car so you can practice in bad traffic (be careful!!!).
When you hear a drummer and he's playing fast, it probably isn't fast to him, so try not to think fast; think deliberate.
The faster you play, the more you start leaving out, especially in the ride hand, and knowing when to start leaving out stuff is key to being able to play fast without getting your head in a tizzy. If you think that way you can play any tempo calmly.
A friend of mine who played with Buddy Rich said that at the fastest tempos they'd start counting only the first beat of the bar: one - one - one... now that's fast!