When sprinting, notice that your weapon is not pointed straight ahead. You can't fire while running.
You will have to move around in order to complete your objectives. Within the single-player game, you can be in three different stances.
These stances affect your speed of movement as well as how large of a target you present to the enemy. While standing, you move at a walking pace.
To move quicker, press the sprint button while moving and you will run. While sprinting, you can't fire your weapon, but are more difficult for the enemy to hit.
The second stance is a crouch. While crouched down, it is more difficult for the enemy to detect and hit you. However, you move slower than while walking.
Finally, you can drop prone onto the ground. If you come under fire while behind low cover, drop prone to make sure you don't get hit—especially if you are trying to recover from some previous hits. Prone also allows you to get under some low obstacles.
One of the cool new mechanics in Medal of Honor is the slide. When you are sprinting, you can slide into a crouch by just pressing the stance button. This will cause your character to quickly drop down into a crouch as he slides to lose momentum.
Learn to use this tactic as you are moving from cover to cover. Press the stance button just before you get to the cover and you will slide the rest of the way in. You are then ready to start shooting at the enemy.