This instructable will show you how to make a simple sequencer that plays a little melody. You can hear how it sounds here:
It is up to you to modify the code to do many other things. Possible examples could be a midi controlled synth (sample code included), it could be a strange noise machine like this one:
Or you could detect touch and convert it into sound patterns:
Step 1: Parts
Don't worry if you don't have the exact values. It will probably work, but might be with lower sound quality. The Arduino is not powerful enough to drive a pair of headphones so you will need some kind of preamp for that - e.g. a headphone preamp like this one.