Practice is key, but I think the most important thing is keep trying if you suck. Everyone has to start somewhere, so expect beatings, expect to have your ass handed to you but crucially try and be objective about why you died. Look at what you are doing and change tactic because you won't ever progress if you keep making the same mistakes. To that end, CO-OP play is very helpful as is team play in online games. When I started BF4 I didn't have a clue, but the guys in the OCUK squad really helped me develop. I still suck but I can rep like a pro now though!!
Arma III really is not a good game to play for someone who is new to or not very good at FPS games. It can be increadibly difficult even for seasoned FPS players. Don't bother with that until you get a bit better.
Perhpas try and pick a game with simple mechanics and try and instil an "I can" mindset. Walk around the corner into a few enemies? What have they got that you haven't? Run in and kick their heads in!
Keep moving. Think about positioning, cover, and where your weak spots are if against multiple AI. Prioritise them and take down the ones that pose the most threat then mop the rest up. Make sure before you get into a fight (if you can) your weapons are always fully loaded and whatever other armaments and abilities you have are selected and ready to use (IE grenades, cloak, shields etc etc)
Get some headphones if you don't have any already. Sound is a huge part of FPS titles and the difference between speakers and a half decent headset is night and day.
Find a mouse sensitivity that you are comfortable with and make sure you have enough desk space to go through full 360 degrees without having to lift the mouse if you use a low sensitivity.
Practice your movement, practice using your loadout. IE move from point A-B, change weapon fire at target Z then throw a grenade over obstical C, duck behind cover D, change weapon pop up and kill imaginary target X. When I used to play a lot of Q3 I used to play on maps on my own to practice aim and movement. Pick a target and hit it whilst moving or using jump pads etc.
Playing an FPS title boils down between the fusuion of what your hands are doing with what your mind can process in terms of what is going on around you. Remember the first time you tried to drive a car? I bet it felt like rubbing your belly and patting your head didn't it? Once you got the hang of it the physical aspect of driving becomes second nature and allows you to properly focus on your environment and react to situations accordingly.
Playing FPS games is exactly the same. You need to hone your ability to control your character to the point you can do it without thinking and then you will find you have far more focus available for everything else and you will panic far less. As you play more and more FPS you start to learn the formulas. You start to develop a spidey sense and start preemting those traps and scary bits
So keep practicing and don't give up. Nopbody picks up the FPS genre and is instantly good at it. True, some people are naturally better at them, but anyone can easily become proficient and enjoy themselves. I have played FPS titles for over 20 years and I am simply average. Good enough to hold my own but my overall ability is average compared to many better players. But I am comfortable with that because I long ago accepted there are plenty of people out there that can kick my ass. I try and learn from them where I can, but often it comes down to base ability and instinct and some people have it. I don't
