If you just want the stump out cheaper than paying someone to grind it off, do you have, or know someone with, a chainsaw?
You don't particularly need a saw with a bar that is significantly longer than the diameter of the stump. I use my 16 inch bar chainsaw on stumps that are wider than this without problems.
If the stump isn't already cut down to within a foot (30cm) of the ground (or even better if it is shorter), do that first.
Now you want to do vertical cuts into the stump in a grid about 2-3 inches (50-75cm) apart, i.e. one set of parallel cuts in one direction, then another set at right angles.
You can start the cuts with the tip of the chainsaw - you start by "drawing the cut with the tip from the side of the stump away from you, and move it back in a straight line toward you (be careful, this is where kickback can occur, particularly if you keep pulling the saw back toward you till it drops off the top of the stump).
Alternate tip cutting with horizontal cutting to even up the depth of the cut, but the tip cutting will do most of the work. The chain needs to be sharp to do this effectively, and if it is then the task is pretty effortless.
If you clear soil and rocks away from around the edge of the stump you can keep the tip cutting pushing down to below ground level. Of course there might be some spaces in the top of the roots under the stump where there is some soil - for this reason I use an old chain on my saw when I do this.
Once you've got the stump gridded with cuts down to at least ground level you have a choice - you can leave it this way to rot down (which will happen much much quicker than before because you have opened the stump up to water and air), or you can attack it with a sledge hammer or a crow bar (don't know if these terms are internationally used, but Australians will know what I mean for sure) to break off the tall narrow "blocks" that you have created - stump's gone. Unless, that is, you want the roots out too. That entails quite a bit of digging and possibly chainsawing individual roots.