For movement, there are 3 keys you need to have easy, quick, and comfortable access to -- keys that you can hit in rapid succession for long periods of time without getting cramps in your hand. Those are the keys for strafe left, strafe right, and jump. Personally, I find the spacebar too flimsy for that, so I have my own fairly unique configuration:
A = left, S = forward, D = right, F = jump. That way I have quick access to the most commonly used keys right on the home row, and it won't cramp my hand. This probably won't work for most people, though. Just sit down and find keys that are comfortable for you, then start up a map and practice jumping around.
Of course, there's a lot more to the game than your ability to move around, but that certainly helps. As far as shooting people goes, I think the most typical mistake is to not lead your target enough. Not only are they moving, but there is a delay between what actually happens and what you see, due to the fact it has to travel across miles of wire to get to you.
As for the physics. There's a few things to note: While in the air, if you're pushing down a directional key, you continue to accelerate, but on the ground you're locked to a maximum speed. While in the air and holding down two directional keys (such as forward and strafe right), you accelerate more than with just one. While in the air holding down two directional keys and turning slightly into the direction you're strafing (ie, forward, strafe right, and turn right slowly), you get even more acceleration. You just have to figure out how much to turn, and keep jumping so you never really touch the ground.
Also, going up hills and ramps can help speed you up / jump higher, since the physics only take into account your horizontal movement, not vertical, so you can use ramps to launch yourself into the air. You can also do "double jumps", where you jump onto a box, and while you're still moving upward, jump off the edge of the box, propelling you even further into the air.
There's a lot of things you can do with the quake2 physics. You just have to practice them.