People that have started playing FPS games need the best aim. In a crucial over 60 frames per second game, any FPS game including the COD series needs real aiming. The key to this is lowering the default sensitivity. In this case Modern Warfare games default to “5” sensitivity. Lowering it can attain better aim. You can easily pick out a camper at long range with a few bursts of the M4. But there are also factors on how these things work. Also with hardware, it should also be adjusted accordingly. A good mouse and mouse pad is also important.
Having to do a lower sensitivity after playing for years on the default one is daunting. It needs some exercise and by that, having to lower it softly rather than just one go. Start with just 3. A headshot can now be an easier to achieve. We humans can only do so fast with aiming (typically 160 milliseconds to hear and about 190 milliseconds to see). So having 5 as the default sensitivity is really more confusing as the screen sometimes is moving too fast. Unless you are born with the gift from the movie Wanted (2008), but then again, nobody can have reflexes as fast as killing a fly wing with a gun.
Here is how to set toggle the sensitivity:
Call of duty 2/3/4/5: Press the Tilde ~ button below the esc key and type /sensitivity 3
Modern Warfare 2/3: Options > Control > Mouse Sensitivity > Slide it halfway of the default value
Once set, you could always practice over a multiplayer map with no opponents. Try to practice about swerving to the spot where enemies typically show up and always right click to aim as this is no Counter Strike. Get the feeling of moving with the keyboard and aiming with the mouse. Put some rounds over that direction with minimal ratio to your preferred guns’ recoil. Some have awful kickbacks that needs some practice especially the ones with high damage.
After getting settled in with the feel of lowered sensitivity, experiment on lowering it further to 1 or as low as .44 (this is my preferred sensitivity). Your mileage may vary. Try to practice again with the new setup to see if it fits your playing style. Get your own preference of mobility over accuracy. Having a bigger mouse pad helps with low sensitivity. This setup has better use with guns that have minimal recoil. So with a typical COD game, an M4 or M16 can do the practice job and progress on your suitable weapon of choice once you adapt to the setup.