Pet departments and stores sell various items in the "Rodent" section. One of my hamsters' favorites is called a "Veggie Wheel." It attaches to your hamster's cage for easy and firm accessability.
Hamsters also enjoy a good doggy buiscut/chew. Just make sure that any product you buy your hamster does NOT contain GARLIC. Garlic is toxic to hamsters.
Whatever you supply your hamster to gnaw on, make sure he actually likes and uses it. If a product goes unused, try something else. (Many hamsters prefer to gnaw on the bars of their cage- harmless to the hamster, but VERY annoying to the human...)
If your hamster will not use the gnawing "things" you supply him, and his incisors become overgrown, he will most likely stop eating and become lethargic. In that case, you will need to dip into that vet fund, discussed on THIS page.