You'll need a saw to cut the trunk and a shovel to cut and dig up roots. Have extra blades on hand as palm wood can be difficult to cut. You may want gloves to protect your hands from blisters and a wheelbarrow to transport the trunk and the root ball. f you are going to use a power saw, you'll also need protective gear for your eyes and ears.
Use your saw to cut down the trunk. Leave at least 2 feet of stump. If necessary, cut the trunk into smaller pieces for ease of handling.
Begin by digging a trench around the stump. The trench should be about 1 foot from the stump and 1 foot deep. Work your shovel under the root ball all the way around the circle, using the shovel to sever any roots you encounter. Use the shovel to pry up the root ball, while using the remaining stump for leverage. Pull and cut any remaining large roots you can see and tamp fill dirt into the hole.
Check local ordinances before burning the palm tree or disposing of it as yard waste. Some landfills cannot accept palm wood. If you decide to use the palm wood in a fireplace, dry the wood for one or two months first. If you use a stump grinder, feed in the stump slowly and carefully.