If you aren't that good at any particular FPS game here is where you can get some common useful knowledge.

Multiplayer  Tips

Weapons-Know your weapons and guns. Where are the best weapons?

Secrets- Are there any secrets that will help you? Any good vantage points. Check areas.

Health/Armor- Look for areas that have health/armor so you can easily heal. Know how the game uses health and if there is any regeneration. Watch your health and make sure it doesn't get too low. Fallback

Good fighting areas- Where is most of the action at? That is where you will have the most success. Don't rush if you aren't prepared get the overall feel for things. Be at one with the game

Paths- What is the easiest path from one point to another? How will you escape if needed. Don't let yourself get cornered.

Game- Know the game type you are in whether is is capture the flag or deathmatch.

Allies- make friends they can help you and protect your back.

Thats what I have for now. Feel free to list your own. I know not everyone will use these but I think they can be very useful.

Well, I have a few:

"The Gun Gamble"
You should try every different type of gun and every gun in that category. I call it "The Gun Gamble" because you be good with shotguns in MW3, but better with sniper rifles in Black Ops. it's really what guns you feel most comfortable with.

"Know Your Position"
If you are using a sniper rifle, you had one of two options: camp like a n00B! or go from place to place, cover to cover, getting kills (my preference). If you're using a SMG, you should stay back a little, rackin' up assists. After you get some ways into the map, then you can start coming farther up to the action. Etc.

"DONT BE A CAMPER!"
Please, just don't-please...

Game Variety- Don't just play one game try some others you may get better at multiple games and you will be bored less often.

if you want to become good in a FPS, then set the settings that fits your gameplay best. it diffences on eatch games what settings works best for you. if possible, edit the .ini files to your likings.
it might take a month or 2 to set them. so don't play whit the settings if your only want to play the game for a little while. because then you will only **** up the gameplay and the game gets worse.

also try to make pro friends that can help you set those settings.
when youve done it in 3 or 4 games. you are able to do the same for other games by yourself.

I win the round, because I make this:
http://www.youtube.com/watch?v=mGwYkX5Aq5k

(Just kidding :P).

I have some experiences in Battlefield 3 and C.O.D-like games.

1) Reaction
Your hand-eye coordination is used most of the time in these kinds of games. As you play more, your reaction will improve. Unlike me, checking to see where I'm gonna settle down.

2) No camping
No camping. Well, there's no such thing like camping in Battlefield 3, but thou shalt not camp! You won't get as many kills as other people, really. But, you can just sit at one place and move on. It's like "Know Your Position" from TDOG422.

3) Obviousness
Enemies can expect you from the centre of action, maybe in a building or a park. Find your way at the sides, not through the middle. In some games when shadows are a must for graphics, you can hide in the dark and pick off people from nearby. But, once again, don't ever camp.

Hardware Information- Know what the best hardware and software is for your game and update it. This will ensure that your game is running at top performance.

Internet Connection- Know your internet and what server would be best to connect to. that way you don't have any unexpected lag.

Game- Make sure you are running the latest version of your game. If you want to play online this is necessary.

Customization - Don't stay with default crosshairs and weapon skins. Figure out how to customize them to your liking.

My number 1 tip for FPS games would be to relax and not rage every time that you die.

Don't sit in front of the screen forever or your eyes will probably hurt or you might have a slight headache

Mine is to use good heaphones or have a really good sound system for tracking footsteps, if possible disable the HUD because it just takes up space on the screen where you could otherwise spot eneimies, disable gun drawing for the same reasons, memorize the hitbox of characters and speed of you bullet, try to get a feel of the distances (a good way is to measure the distances in time the bulet takes to cross it. Know who you are playing with, generaly kids do worse at video games and make more newbish mistakes so you'l be able to change your strategy for that, for older peeps let them kill you about 3 times to get the feel of how they play so you could have a counteracting strategy.
Know what paths are usually taken so that you'l be able to predict where someone will be, if it's a 1v1 then its a really good idea to talk with them to figure out what type of player they are so you could focus more o how to counteract the way they play.

don't quickscope or mod/hack everyone will hate you and what's the fun in flying around with limitless health killing people there's no skill to it and everyone will leave or report you or something there's my tip