Cut off as much of the top of the stump as possible. Using a 1-in. spade bit with a spade bit extension, drill 1-in. holes around the perimeter of the stump about 12 in. deep and 3 to 4 in. back from the edge. Drill more holes 3 to 4 in. down from the rim at a 45-degree angle to connect with the other holes. They'll provide vent holes for burning or help the rotting process.
You can remove a stump by renting a power stump grinder, but another way is to buy a can of stump remover (available at most garden or home centers). Most brands are made of powdered potassium nitrate, which speeds up the rotting process. You simply pour the granules into drilled holes and fill the holes with water. The stump will become pretty spongy after four to six weeks. Keep kids and pets away. Then you can break out the rotten wood with an ax.
For a completely labor-free removal, the manufacturers of stump remover suggest burning out what's left of the stump by pouring kerosene or fuel oil (never gasoline) into the holes. Wait until the liquid completely penetrates the wood (this could take a few weeks). Then drop a match into the holes to start the burning process. The stump will smolder for days, eventually leaving a charcoal-filled hole. It's dangerous having a giant, smoldering ember in your yard, so some precautions are in order. Envelop the stump in chicken wire, remove all leaves from the vicinity before ignition and keep an eye on it!
We suggest the ax method for finishing the job. Stump removers work only on seasoned (older) stumps that have been dead for a year or so, not freshly cut tree stumps.