I was a starter throughout my college years and for three years after that, but I spent my last summer closing games. It helps to really pay attention during the game, watch hitters and find out their tendancies. Try to envision how you would get that hitter out and what pitches you would throw him. How you would set him up to get himself out. Try to look into the future when the game is going on to see if you think you will be pitching that day. If it's a close game, you might get "focused" a little sooner than in a blowout.
From a physical standpoint, have a routine. Stick to that routine and be physically ready to pitch when the coach calls on you. Never be caught off-guard. This will help mentally as well.