When a tree has been removed, all that's left is the stump. If a professional tree service was used, they will probably have someone come by later to grind out the stump and leave a big pile of wood chips. However, this doesn't always happen. If you were the one that removed the tree, there won't be someone else to finish up the job. What you need is a tree stump removal strategy. You can rent a stump grinder, but they're expensive and can be dangerous if you don't know what you're doing.
Manual tree stump removal is cheap, but labor-intensive. Instead, another cheap alternative that is also easy is available. But be forewarned: this tree stump removal method requires some patience. Actually, there are a couple of methods depending on the amount of energy you want to expend.
Tools: chain saw, axe, mattock, shovel
Manual tree stump removal uses a hefty mattock. Its broad end allows you to dig around the stump; the other end functions as an axe for chopping your way through tree roots. Dig and chop your way under the root ball to the taproot. For large tree stump removal, taproots may be imposing enough to require cutting with a full-size axe. This method takes time and a bit of endurance. All you're trying to do is remove the central mass of the stump and not all the main roots that spread out through the ground.
Tools: drill, large drill bit, high nitrogen fertilizer, heavy plastic (tarp), mulch.
Wood that isn't alive will eventually rot from moisture, insect activity and natural microbes, but depending on the original wood, may take a number of years to accomplish. This alternative removal method is essentially one way to hasten the natural processes. It doesn't work over night, but within a year, with any luck, you'll have reduced the massive tree trunk to a soft pulp that you can just ignore, or safely remove it with the mattock and shovel.
To speed up the natural process you’ll be adding 2 ingredients in unnatural quantities that when combined will speed up the decaying process. Those ingredients are nitrogen and water.
Using a chain saw, carefully cut the stump down as close to the ground as possible. Don't allow the saw's chain to strike the ground (this dulls the chain very very quickly). Once the stump is leveled off, drill some holes at least 2" deep or more, into the stump in a number of places, using your widest drill bit. The more, deeper and wider the holes are, the better.
Fill the holes with water, then comes the fertilizer which should be high in nitrogen. If using a commercial fertilizer, make sure the first number on the bag is the highest. Pour this fertilizer into the holes. Next, soak the ground evenly around the stump.
Cover the stump with a plastic tarp, either black or clear, since it will be covered over with a sheet of plastic. The tarp acts as a barrier that will help keep the area and the wood moist. Plenty of moisture is a powerful ally for tree stump removal.
Cover the plastic with an organic mulch, and dampen it thoroughly. Any organic mulch will do, such as wood chips or shredded bark. This mulch will help hold in additional moisture keeping the area even wetter. Wet mulch will keep the tarp in place. If you have a few large stones available, roll them onto the tarp.
The final step is patience. The above steps greatly speed up the natural rotting process, but it will still take some time. Then sit back and wait for completion of your tree stump removal project.
Periodically repeat the process: remove the mulch, plastic and add more nitrogen, then re-apply the plastic and mulch. Soak the mulch again, too, to keep the tarp wet and weighed down.