Hmm. I haven't got/played MW3, but I did play MW2 a great deal, as well as Blops and BC2 to some degree.
In both MW2 and Blops, I favoured a stealthy approach and using the terrain and my cammo to remain undetected by UAV's, various killstreaks and from the very enemies I was fighting.
I know that MW3's perks have been changed a great deal, but if I was to play it today I'd still focus on Blind Eye, Assassin and Dead Silence, along with a silenced weapon of some kind.
I've always found that the element of surprise and minimising the enemy's ability to detect you was more beneficial to my playstyle than going for more accuracy or damage. However, everyone is different and has different playstyles.
The main issue with all FPS games is positioning. A good portion of any FPS requires the use of good strategic and tactical positioning and awareness of the most likely areas and ways in which the enemy will hide/move through. High traffic areas in general you wish to avoid. You'll want to be on the outside of the map unless you're playing a more teambased game such as DOM or CTF.
You need to be aware of the sightlines in all the maps you play, and try to minimise your travelling time in open ground and always try to pick a route that gives you the best possible protection when reaching your goal. Knowing the sightlines allows you to predict how and where a potential enemy can strike from.
Also, I'd like to say that knowing when to retreat and when to attack is important too. Don't try to take on 4 people at the same time and charge them. Nine times out of ten it simply won't work. If you don't hold the advantage in a situaion retreat and regroup. Chances are the enemy will smell blood and try to chase you; you can then capitalise on this.
Be aware of flanking and counter-flanking maneuvers and act accordingly. If your teammates are attacking/defending a certain point, keep a look out on the other paths and routes to your location so you can cover them and don't leave yourself or your flanks open. Try and protect your blindspots by utilising sentries, claymores and other equipment. One tactic I used to use was laying down claymores to protect my blindspot. If it went off, regardless of whether or not it killed the person, I knew that I was in danger and could act accordingly.
Sounding was also for me very important. Knowing who is where was important to my playstyle. Everytime I heard a sound of someone running, moving or reloading I would reference that sound to the UAV's information. If a teammate was nearby the area that the sound originated you can breathe easy; if there isn't a teammate close to that area, try and predict where the enemy will come from and put yourself in the best position you can in order to attack them.
This is fairly basic stuff, but I hope it helps. Remember though that at the end of the day, you learn from experience, even if it does take hundreds or thousands of repetitions to do or understand something correctly. Be positive, keep calm and play the game
