Shut off the main water supply valve. Attach an adjustable wrench to the valve, and turn the valve 90 degrees clockwise. Open the leaking outdoor faucet and allow the existing water in the line to drain.
Grip the pipe below the faucet with a pair of pliers. Tighten a pipe wrench around the faucet and twist the faucet counterclockwise until it is free from the pipe.
Clean the pipe threads with a stiff-bristled brush. Rinse the threads clean with water and dry with a towel.
Wrap the cleaned pipe threads with plumber's tape. Start at the base of the threads and work your way toward the end of the pipe.
Tighten the new faucet by hand. When the faucet is hand-tight, wrap the new faucet in a towel and tighten the faucet as much as possible with a pair of adjustable pliers. The towel will protect the finish on the new faucet from the pliers.