How big is the stump? If it is a full size tree you will most likely end up renting a stump grinder or having someone come out and take it out.
If it is smaller, like 6" at base and roots no bigger than 2-3" (like mine) than you can try my method, which worked perfectly if I do say so my damned self. Here it is. . .
Take an old shovel head, or buy a cheap regular shovel (not the flat, squared of edge, but the kind of pointed one) and remove the handle by hook or by crook - it can be hard to get it out of there, but keep trying. Now go to the plumbing section of your local home improvement place and get a 6 foot piece of STEEL pipe (not aluminum) 1" in diameter, or slightly smaller than the hole that the handle came out of. Also get 2 or 3 sturdy metal hose clamps, the type that you screw and the threads engage slots in the band of metal and tighten.
Now, if you have a vice or something to hold the shovel head, try and pry open the end that the handle goes in a little bit with a prybar. If you can't do this it is OK, it just makes the next step a little more effective.
Put the 2 or 3 hose clamps over the end of the shovel head where the handle goes and cram the steel pipe in as far as you can where the handle used to be. Now if you have a vise, put the handle section of the shovel head in the vise and sinch it down tight on the pipe. When it's as tight as you can get it, tighten down the hose clamps as tight as you can. Now take a dremel to the shovel edge and sharpen.
If you were lucky enough to get a piece of pipe that was threaded on one end, leave that end exposed and you can put a cap on it and fill the shovel with sand for more weight. I haven't done this as the steel pipe was enough weigth for my wimpy a$$.
This thing works like a dream for smaller stumps. Sorry for the long and idiot proof instructions, just wanted to be clear on everything. Now start digging!