Turn off the water supply to the garbage disposal. Use a 3/8-inch wrench to remove the screws holding the discharge tube to the disposal.
Unscrew the sink's P-trap from both the discharge tube and the drain pipe. Unscrew the drain pipe from the water pipe.
Remove the old plumber's tape from around all pipes. Wrap new plumber's tape around the screw end of the drain pipe, wrapping clockwise. Screw the new drain pipe onto the water pipe by hand as far as you can and use tongue-and-groove pliers to finish tightening it.
Wrap plumber's tape around both ends of the P-trap, wrapping clockwise. Screw the trap to the drain pipe by hand and tighten with the pliers. Screw the discharge tube to the P-trap.
Push the discharge tube onto the garbage disposal. Insert the screws and tighten with a 3/8-inch wrench to hold the tube in place. Turn the water supply back on.