Strike the top of the tree stump with an axe. You want to cut off as much of the rotted stump as you can.
Remove the dirt from around the perimeter of the tree stump, using a shovel. Dig deep enough to expose the tree roots.
Cut the exposed tree roots with a wood saw. Cut off all the roots. Shovel away any debris.
Dig around the area at the base of the tree stump. You want to be able to get the shovel underneath the tree stump.
Push the shovel underneath the tree stump and pull down on the handle so you can pry the stump out of the ground. You can place a piece of wood between the head of the shovel and the ground for more leverage if necessary.
Remove the tree stump from the hole when it breaks free. Set the stump off to the side. Backfill the hole with soil.