Removing a tree or stump doesn't always require calling in a professional--and no, we're not talking about chaining it to your truck and bearing down on the gas pedal. Properly removing a tree or stump requires a series of carefully calculated steps and can take several hours, but it also can save you a ton of money.
The Right Equipment
Don't even think of removing a tree or stump without the proper equipment. You'll need a good pair of pruning shears, capable of cutting branches up to 1 1/2 inches thick; a pruning saw; a good-quality spade and a landscape bar, a useful tool with one pointy end and the other end flat and sharp, for cutting. You also might want to invest in a good pair of garden gloves, made of hardy leather, and steel-toed boots, just in case the stump falls on your foot--or you drop your landscape bar right over your big toe.
The first task at hand is to remove as much of the vegetation as you can. If you're yanking out a whole tree, start your way at the top and work your way down, focusing on cutting off complete branches. When you're left with a bare vertical stem or trunk go back and clip or saw those branches apart for easy disposal. Leave your bare vertical stem or trunk--in some trees, you might be left with two or three of them--about 4 feet high, to give you leverage when it comes time to rock the stump for removal.
Preparing the Stump
Start digging a trench around your stump, making your shovel do double duty by both removing dirt and chopping off roots. Work your way around the stump at least a foot away in a clockwise or counterwise direction; when you're done, go back and do it again, going deeper each time. Be sure to fling the dirt away from the tree, so you can expose as many roots as possible.
Attacking the Roots
When you've dug three or four times around the stump, start using your pruning shears to cut away roots. For big roots use the landscape bar, both its sharp end (to cut) and its pointy end (to pry). In fact, it's a good idea to keep circling the trunk again, this time with the landscape bar, thrusting its sharp end into the dirt to cut any unseen roots as well as the visible ones. Circle around again, and again, thrusting inward each time until you reach the center of the stump. At this point the stump will start to get loose and might even rock and sway with each thrust. This is a good thing--a sign that you're almost done.
When the stump is sufficiently loose, or after you've been around the stump with your landscape bar enough to penetrate the center the entire way around, put your tools away. Now comes the easy part: pushing and pulling on that 4-foot-tall section of trunk until the remaining roots break free and you can tug the stump right out of the ground.
For really big stumps, you might want to use a stump grinder, which uses a high-speed disk with specially designed teeth to grind the stump and roots into tiny chips.