Visit your local tool rental center and rent a stump grinder. Read the operator's manual that was included with the stump grinder. Familiarize yourself with the buttons and controls. Read and follow all warnings and directions.
Examine the chainsaw blade for nicks, damage and sharpness. Replace the blade if necessary. Fill the chainsaw with the appropriate fuel.
Don a pair of safety goggles and heavy work gloves. Turn the chainsaw to the "On" position and start it as you normally would.
Hold the chainsaw firmly away from your body and begin cutting the stump as close to the ground as possible.
Remove debris -- such as sticks and rocks -- from around what is left of the stump. Place the stump grinder in the front of the stump with the wheel raised 3 to 4 inches above the stump, but keep the wheel as close to it as possible.
Turn the grinder to the "On" position and let the wheel begin to spin. As the wheel is spinning, lower it on to the stump and begin moving the wheel in a slow back-and-forth motion. Continue moving the spinning wheel -- while lowering it as needed -- until the grinder's teeth has chipped the stump 6 inches below the soil.
Turn the grinder off and move it away from the stump. You can dispose of the left over wood chips, mix them with the soil or rake them up and use them for mulch.