Chainsaw the tree down to a stump as low to the ground as possible.
Drill holes at least 6 inches deep into the stump. A stump under a foot in diameter may only require four to five holes. A larger stump should have 15 or more holes.
Drill holes into any exposed roots. Larger trees may have many roots or knots exposed over the surface. You can dig these out or allow decomposition to deal with them.
Pour nitrogen-rich fertilizer into the holes. The nitrogen feeds fungi, which will promote the decomposition of the wood.
Cover the tree stump with a tarp or compost so that it retains moisture. Both the moisture and the darkness will promote decomposition.