Cut the stump as low to the ground as possible
Drill deep holes into the stump
Fill the holes with stump remover or high-nitrogen fertilizer
Soak the stump with water
Cover the stump with a tarp to retain moisture
Wait several weeks or months for the stump to soften and decay
Chop the softened wood away with an axe or mattock
Dig around the roots and cut them with a saw or loppers
Pry out the stump with a shovel, digging bar, or stump puller
Use a chainsaw to cut remaining roots if needed
Rent a stump grinder and grind the stump below ground level
Remove the wood chips and backfill the hole with soil
Hire a professional for large or difficult stumps