Connect it to your computer and open iTunes. If the iPod stays on, you can select it in the left sidebar and then click the Restore button to restore it to its factory settings, bearing in mind you'll have to re-download apps (for free because you already bought them), redo your settings, etc. Music shouldn't be a problem because it only syncs with your iTunes library... unless you bought music on the iPod itself... in that case you might have to buy it again depending on what synced and what didn't.
Anyways, if you're still having trouble, make a Genius Bar appointment at the Apple Store (link below) and they'll be able to run tests and stuff on it. If you're still under warranty you're covered, but even if you don't have warranty anymore (you should if it's under a year old) they will probably only charge you to fix it. A certain fee, depending on what the actual problem is.