Remove the old shower head. It's connected to a pipe that extends out of the wall. Grasp the pipe behind the shower head with one hand, and using your adjustable wrench, unscrew the shower head where it connects to the pipe with your other hand. Keep the pipe steady as you unscrew the shower head to avoid damaging the pipe.
Place the old shower head somewhere that you will not lose it. Save the old shower head because it belongs to your landlord, and you can replace your new shower head with the old one before you move.
Wrap the pipe's threads with the thread seal tape, wrapping two to three times. It is important to get a good layer of thread seal tape on the threads to create a seal that will prevent the shower head from leaking.
Place the new shower head on the pipe and carefully begin to thread the shower head by hand. Once the shower head will no longer turn by hand, grasp the pipe behind the shower head with one hand and tighten the shower head with one twist with the adjustable wrench. Ensure that you keep the pipe steady to prevent damage to the pipe. Also, do not install the new shower head too tightly or it can break, or damage the threads on the shower head and the pipe.
Turn the shower on to see if it is leaking where the shower head connects to the pipe. If you see a leak, make sure the shower head is installed properly and the connection is tight.