Their are a number of different ways to hold your drum sticks. The more commonly used grips are matched, and traditional grip. Matched grip is a method in which both sticks are held the same way, whereas in traditional grip, each hand holds the stick differently. Matched grip is done by placing both sticks in the hand palm facing down and wrapping your fingers around the sticks leading with the index finger. Matched grip allows you to use your fingers as a fulcrum when playing.
Traditional grip is each hand holding the drum stick differently, the right hand uses the same method as matched grip, and the left hand uses an under hand hold. The left hand holds the stick between the thumb and index finger, middle finger should be extended and the stick should rest on the ring finger. This style of playing is most often used in marching and jazz bands.