The hard way....
Shovel, post hole diggers and a sharp axe. Dig a hole as close as you can to one side of the stump and as deep as you can. Dig it with the idea that it is going to be the source of air to a fire that your going to build and since heat rises, the deeper the better. Make sure you dig it deeper then you will ever till the land and light a fire using some firewood, limbs, etc. Just keep it burning and the stump will be gone, and the roots will go with it if you keep the fire hot enough. If you have a piece of steel pipe that you can stick a leaf blower into, put it in the bottom of the hole, but make sure it is long enough to keep you away from the heat and flying embers when you add air to the bottom of the fire.
Doing it this way takes a lot of time and effort, so a backhoe is the next best thing to dig all around it and then pull it out.
David from jax
If you have a rocks in your soil, then this is a waste of time, as digging is way too hard manually.