Corinna, take several images of the moon with the same settings (remember a faster than expected shutter speed) and stack them all on top of each other in photoshop.
The more images you get the clearer your finished photo will be. It's not unusual to stack 100+ images but it takes a bit of time.
Also as soon as you've taken your shots of the moon put the lens cap back on and with exactly the same settings on the camera take a "blank" photo. (Dark Frame) In photoshop subtract this dark frame from you finished, stacked photo to remove most of the digital noise.
Finally try not to oversharpen images of the moon. The craters may seem very small and like little sharp dimples but in reality they are quite large with few sharp points smaller than a huge rock!