Claves are a deceptively simple percussion instrument that are found in traditional and contemporary musical genres all around the world. Simply put, the claves are two sticks which are "clacked" together to make a sound.
To play the claves, you can simply hold one in each hand and strike them together, or you can play them in a more traditional Cuban style, where you cup one flat against the palm of your left hand, which is held still, and strike it with your right hand.
Experiment with holding the sticks more or less tightly, "choking up" and holding them higher and lower, and letting them resonate for longer or shorter periods of time. There's a surprising amount of tonality that can be pulled from these simple instruments; after you've experimented a bit, you'll realize how complicated the job of the claves-player really is!