Dig around the stump with a shovel or grub hoe. When the tree's roots are exposed, saw them off of the stump using a root saw, then pull the stump up and out of the ground with your hands. This is an effective method for small trees or trees with shallow root systems.
Rent a stump grinder from a local hardware store. This machine can grind a tree stump up to 12 inches below the ground level, which is ideal for small and medium-sized tree stumps. Always read the grinder's operating instructions completely, to operate the machine safely. Once you begin to grind away the stump, keep grinding until all of the main roots have been chewed. The stump will be a pile of wood chips and pieces, which you can pull up and out of the ground with your hands or a shovel.
Drill large holes into your tree stump with a boring drill or large drill bit. Fill the holes with kerosene or fuel oil, though never gasoline. Wait several weeks until the fuel penetrates the stump, then carefully drop a match into one of the holes. With this method, your tree stump will burn away down to its roots. When the stump has burned away, remove the rest of the wood chips and ash with a shovel. Make sure there is nothing that will catch on fire near to your stump, such as garden plants, other trees or home structures. The burning method can take up to three days, depending on the size of the stump, and will not usually work on freshly cut or young tree stumps, since they will not catch on fire.