Playing COD2 a lot, it's pretty similar to those games.
Tips:
I use a ridiculously high sensitivity, as I have small desk space etc, but in general a lower one is advised. Just play about until you find one that suits you.
Practice with the weapon you're most effective with, don't use others, unless it's a rifle and you need an auto gun as a backup for people that get too close.
Go prone often, it's harder to be hit
Turn up the sound and use footsteps/weapon shots to your advantage to pinpoint the enemy.
I don't know about other games, but COD2 has an icon that comes up to show you where a teammate has just died which hovers over their body to give you an idea of where the enemy are.
Learn the maps well so you're not lost, and can expect areas where people camp or are often positioned, for example a road which is a link between two major positions.
Learn ways of getting behind these positions(There's usually a way) so that you have the element of surprise.
When going round corners, get ready to aim, so you have the upper hand and are hopefully aiming at the enemies face. (if it's a 90* corner, face the wall and sidestep out, so you're facing the direction the enemy may be)
Use leaning to your advantage.
Use grenades to clear out corners you think you heard someone in, although be careful as they can alert the enemy to your location.
NEVER STAND STILL IN THE OPEN; you will be sniped.
That's the basics.