Use your quick release or axle nut to hold the freewheel removal tool snug up against the notches in the freewheel. This will help prevent slippage. Then, stand the wheel upright and brace the outside of the tire (this method assumes the tire is mounted) against a wall in such a way that when you turn the wrench handle, the tire will be pressed against the wall. This keeps the wheel stressed in a way that it was built to handle. Haul away on the wrench handle, and the freewheel should loosen pretty easily if the threads were properly greased when it was installed. Once you've loosened the freewheel, remove the axle nut or quick release and it should unscrew by hand.

To install the new freewheel, just tighten it hand-tight so it's snug, but be careful not to cross-thread it. The first few turns of the cranks should torque it down just right. Don't forget to grease the new threads before installation.

Cheers!