Summarize this article:

Unlike the Continental method, the American style of using a fork adopts more of a pen-like hold. The handle rests against your hand in between your thumb and forefinger, your middle finger and thumb are holding the base, and your index finger rests on top. Again, the tines are downward, curving away from you. This hand positioning is the same as in the aforementioned style -- with your index finger along the base and your other fingers wrapped around it. If you are eating a dish that doesn't require cutting, keep your fork in your right hand at all times with this method. Tines can face downward if you're taking a bite, but will generally return upward for the majority of the time. However, do know that only in the absolute most formal of settings will this ever be an issue. We're talking when the President is sitting across from you. Other than that, don't stress. Your silverware should never touch the table. If you're only using your fork, be sure your knife is resting along the edge of your plate. When you put your fork down, rest the handle on the edge, tines near the center of the plate.

Summary:
When cutting, hold the fork in your left hand. Only when cutting, place the knife in your right hand. Apart from cutting, eat with your fork in your right hand, tines facing upward.