Get a mate or two to help you. We had a good time removing one in our back garden, coz we looked at it like a challenge.
We chopped it down leaving about three foot of stump (enough to get hold of) and then dug down around the roots and used saws and old chisels (with hammers) to cut through the roots. After about three hours of sawing, chopping, hammering and drinking cups of tea there was a great feeling of achievement as we heard the lovely sound of the last rooty bit snap as we levered the stump out.
Then we cracked open some cans to celebrate and took photos of us standing with one foot on the mighty slain beast.