Dig all around the stump. If the stump is under water, carefully shift the dirt and silt away so that you can reach into the muck around the stump. The goal is to cut all of the roots that you can, and sever as much of the stump's connection to the ground as you can. Move your shovel carefully, ensuring that new dirt and silt doesn't just slide back into the hole you dug out.
Wiggle the stump in its hole. Pull and push the stump like you would a baby tooth that you're trying to pull out of the socket. Using your shovel, or a long prybar, hack at the area holding the trunk in place as you pull and push it.
Wrap a cable or chain around the trunk and secure it to a winch or truck. If you cannot pull the stump out with your own strength, then attempt to pull it out using the traction on a truck as it drives away, or by reeling the cable in with a winch. Do not stand near the trunk; be sure that you're out of the way in case it suddenly comes free, or the chain breaks and lashes out.