It may be all but impossible to dig out a large, deep tree stump. For a large tree stump, professionals use large tree stump grinders. You can rent one, if you feel comfortable with large machinery.
To remove (or to attempt to remove) a tree stump by hand, dig out around the roots as much as possible. Be prepared for some work that will last a few to several hours. Use a large spade but also a trowel to dig around it as much as possible. Saw off the side roots as you expose them. Then, as much as possible, slice off the stump from underneath with a saw. If you're able to sever it from the very large, deep taproot, with the help of another person or two, lift out the stump.Some people use a chain saw to remove tree stumps by slicing away chunks of the stump. This method badly clogs and dulls the chain, and you will most likely need to replace the chain when you're done. Wear heavy gloves, boots and appropriate clothes, as well as eye and ear protection. Be patient and cut off just small chunks at a time to prevent kickback. Take frequent rests and if possible, spread the job out over a period of a couple of days. Dig out the roots as you work and slice them out as much as possible.Ideally, you'd slice out enough of the stump so that it's several inches to a foot or two beneath soil level, but this is often difficult to achieve. If you can get it just 3 to 4 inches below soil level, you can then spread soil over it and plant it with annuals, a groundcover, or grass.