Well the answers are going to depend on which first person shooter you're referring to. Whether it's Call of Duty, Battlefield, or Counter-Strike, they're all going to have their own unique tips that will make you better at that specific game.
However, I suppose there are some general things to keep in mind when playing any first person shooter, like:
1. Always reload when you can. Optimally you want to have a full magazine at the start of any firefight.
2. If an enemy is shooting at you from behind cover, don't just wing it and shoot at them outside of cover. They have a massive advantage over you. Find cover, and return fire.
3. Stick with your team. You vastly improve your chances of survival when you're with other people. Lone wolfing is a good way to find yourself staring down a squad's worth of gun barrels.
4. Relax. Getting tense or angry is a good way to distract yourself from the game, and it'll end up doing nothing but getting you killed.
5. Practice, practice, and then practice some more. A lot of being good at FPS games is in muscle memory, and the only way you'll get that down is through repetition.
