Before you proceed there are two things that you need to do first.
When things are dry, it is much easier to burn so if the stump has not yet dried properly you should wait until it has dried. Before you start the burn, call your local fire department to make sure that you will not be breaking any rules about burning where you live. If it is okay to burn, make sure the stump is nowhere near any flammable materials or close to any building.
Stump burning steps
You will need a chain saw to cut an “X” on the top of the stump. The deeper and wider the X the better for burning the stump. Fill the area that was just made with gasoline or kerosene but do not light it. You need to give it time to soak into the stump, which can take several hours. Once the fuel has soaked in, pour more in the area until it flows over the side and leave it sit overnight. Set fire to the stump the next morning by lighting some paper and tossing it on top of the trench. To make the burn more effective and go faster you can follow the above paragraph but before you set it on fire get a large metal barrel. How big it actual needs to be will depend on how large of a stump you need to burn. Cut off the bottom, top of the metal barrel, and place the barrel over the entire stump. Toss in some log and put some more fuel on the logs so a good fire will start. When you are using the barrel for stump removal, put in more logs once the fire is burning good. The barrel helps to keep a high temperature so the stump will burn more efficiently because it is soaked in fuel. Keep putting in more logs and let it continue to burn until the stump removal is finished. If you need to burn it some more the next day, you can cut another X in the stump or drill some holes in, pour more gasoline or kerosene on the stump and set it on fire again.
If the stump removal involves a stump that is deep rooted and really big burning it out might not work so you may hire someone professional to do the stump removal. Make sure that you wear protective gloves to protect your hands from being burned.