Drill 1-inch wide holes in a ring around the edge of the stump as well as in staggered lines across the top of the stump. The more wood in the stump you expose to the elements, the faster the stump will rot.
Cover the stump with 1/2 cup of granulated fertilizer (10-0-0). The microbes that cause the stump to decay in the first year will use the nitrogen in the fertilizer as food.
Turn squares of sod upside down and place them against the stump. Water the sod with a garden hose so that it remains as damp as a wrung out sponge. The damp sod will create a beneficial environment for the microbes that cause a stump to decay.
Cover the stump with 1 cup of sugar instead of fertilizer after the first year. The microbes that cause the stump to decay will feed on the carbohydrates in the sugar instead of nitrogen in fertilizer after the first year. Eventually the stump will decay.
Dig a trench around the stump that is 2 foot wide and 2 foot deep with a shovel, spade or grub hoe. Sever any roots you encounter using a pair of branch loppers, an axe or a grub hoe.
Push the stump to one side and cut any roots you encounter under the stump with an axe or grub hoe.
Lift the stump from the ground and carry it away. Fill in the hole left by the stump with topsoil.