Turn off the electricity to the well at the breaker.
Turn on your water faucets and drain them. Wait for the water to stop before beginning installation.
Unscrew the pipe underneath the pressure tank with your plumber's wrench. Do this slowly, allowing it to release the excess pressure as you go.
Remove the tank after fully unscrewing the pipe.
Install the new tank in the old tank's place. Wrap pipe thread tape on the threads of the pipe, going fully around three or four times. Screw the pipe into the pressure tank.
Turn back on the electricity and test for leaks.