Tyr this:
Take your time
It's slightly heading towards being a camper, but take your time. You don't need to run all the time, only run at times where you know you are very unlikely to be shot or can do anything about it if you are. It's a little bit frustrating, but then balance that with having to respawn.
For example, stairwells - no point walking slowly up them as someone at the top will slot you more than likely.
If in doubt, flash the corner.
Heard gunfire? Seen dots nearby? Flash a corner before running round it. You always get more flash grenades at respawn
This includes areas that you know there's a likelyhood of someone being there. Going to a point in Domination? Flash it. A flag in CTF? Flash it. Even if you don't actually get the person properly disabled - the hit markers will indicate someone there.
Look for gaps that others won't.
MW3's terrain is quite complex, and there'll be spaces in the fences or gaps in bushes that you'll see before you are seen. Not saying you should hang around them - but they can be useful as you move forward.
Stick to the shadows.
Simples. More difficult to see you if your opponent is in the light and you are in the dark. Also, if you can, mix it up with crouching, dropping or sidestepping on encountering an enemy. Take the initiative from them, make them react.
Think about the map.
Where are the kill zones? Should you be in the kill zones? No, thought not. Big wide open spaces with areas of cover all around? Why go through the wide spaces? Always run that way? Why? Do you think other people will do the same? Probably. What about trying a different route?