Visit your local hardware store. There are a number of stump removal products on the market. One call Stump-out, Spectracide has a stump removal product also.
Essentially, you drill multiple holes at a down angle and pour in the product and wait 8-12 weeks for decomposition to take it's effect.
Once it has become soft and well decayed, you can either dig it out or saturate it with kerosene and let it burn itself out.