Dig around it to expose the thick roots, cut through the roots with a chainsaw, using an old or cheap chain, as the soil will wreck a good chain.
Make sure you have a file to sharpen the teeth as you will need to sharpen it a few times

A heavy duty fencing pike or pole used for fencing. An old hand saw and pick ax. If its very mature and wide spread just hire a stump grinder for the morning won't cost much.Don't attempt using a chainsaw with an old chain it will last 2 seconds and be no good for the piston and pot.

Hi basic tools needed are a spade a good axe a pair of loppers and a trowel. Wet the area around the stump to soften the ground for digging. Dig around the stump to expose the roots and use the axe to sever them. Try and dig under the root bowl with the trowel cutting any small roots with the loppers. Try and lever the stump and root bowl to expose any further roots not yet cut. Eventually the root bowl and stump will pop out. The degree of difficulty depends on the size of the stump and root structure. Persevere you will get there.

Dig the ground to expose the roots and then hit them with an axe to sever them. If you can get your hands on a hi lift jack once you've dug below the root ball they are fantastic to help lift the root ball and rip any remaining roots out. If it's a particularly large stump it will be best left for some form of machinery

A matock and a breaker bar to dig around the stump breaking all the roots until you have movement, cut the stump high so you have leverage to snap it out.