I am a volunteer at a community bike co-op, and this is a common problem that people come in with. It has several possible issues:
1) Maybe nothing is worn out, but the chain is slack. When you look at the chain, is the bottom of it super slack? Do you normally pedal in the smallest front chainring? If so, I recommend trying out a different front chainring to take out some of the slack. Occasionally you see a chain which was not correctly sized, but that is rare.
2) Maybe the chain is worn out. The ruler method mentioned above is good. Another good solution is to shift into the largest chainring and then attempt to pull the chain away from the ring with your hand (sorry, you get dirty). If the teeth and chain are fitting tightly together, then you won't be able to pull it much at all. If the chain is worn out, you might be able to see a little daylight in between.
3) Maybe the chainring is worn out. Do you always pedal in the same front chainring? If so, there's a decent chance its worn out after ten years (I personally ride 90% in the middle front chairing, so I have this issue). You can inspect the chainring to see if the teeth appear "sharper" on that ring than the others, that means its worn out. Sometimes you can replace just one chainring, depending on the type.
4) Other stuff: maybe the chain isn't slipping at all - occaisionaly seen rear wheel ratchet slip for example.
Good luck.