Practice on Official Tourn. CS maps, like nuke, inferno, etc.
Learn how to use the best weapons. Like defendo said, Deagle is probably the best handgun, AK/M4A1 is the best rifle, Magnum/AWP is the best sniper rifle, etc.
Jump like crazy when you're being shot at. You'd be surprised how much you can avoid.
Don't be afraid to walk, especially on small maps. Sound can be a huge key to sneaking up on people, especially those who are camping.
Learn the recoil for your main weapons. For example, the AK has terrible recoil that goes in a straight-up motion. The MP5, on the other hand, has excellent control, and has little recoil.
Master the use of grenades. Know when a Flashbang, smoke, or frag grenade will be useful. Know where to launch one (meet-up places, places where the other team usually comes through, etc.), as well.
Good luck.