Instructions
Press down on the left joystick button (the one used to move your character forward and backward) and hold it as you use it to move your character forward. Your on-screen character will sprint.
Pause your character and stop moving during periods of inactivity. If you've successfully evaded an enemy, give your character 5 seconds or so to breathe. You cannot run indefinitely in "Modern Warfare 2" -- you need to let your character rest for a few seconds so that he can sprint again.
Equip the "Marathon" perk from the "Create a Class" screen during your private match. Perks are only available during private matches and online multiplayer games in "Modern Warfare 2." Equipping the "Marathon" perk allows your character to sprint forward faster and longer without pausing to regain energy.