Practice. A lot.
I play PC FPS. I have friends who play PC and PS3.
The most important thing is to learn the maps. Choke points, power ups, spawn points, objectives, sniping spots, everything. When you move through the map you should know where any threats might be coming from and take advantage of any cover or opportunity the map provides. Play until you are not surprised when you get killed, but think, “Damn, I shouldn’t have tried to go up that stairway without lobbing a grenade into the 2nd story first. There’s always someone hiding up there!” You have to make every map your home turf. Know your maps.
Master doing a 180 to look behind you without changing direction of travel. You need to be able to run backwards through the map as well as you run forwards.
Never stare in the same direction for too long. Always look around. If you’re facing the same direction for more than 5 seconds without shooting you need to look around.
Don’t get discouraged by where you come in the scoreboard. If you’re playing solo against clans, or friends, or people who are using voice for teamwork you’re not going to rank high. Join a clan, find some people to play with. Use your mic for teamwork! It’s pretty easy to make friends in FPS and it will up your game tremendously.