Turn the power off to the kitchen at the breaker box. Make sure that you label the breaker so that no one accidentally turns the power on while you are working. Remove the existing S-trap from the drainpipe using a pipe wrench. Remove the tail piece from the sink strainer using a pipe wrench. Remove the retaining ring from the sink drain by tapping on the notches with a screwdriver until the ring is loose and then twisting it counterclockwise to remove it.
Remove the drain basket from the sink bowl. Spread plumber's putty around the bottom of the ring of the disposal drain piece. Insert the drain into the opening of the sink bowl. Install the gasket and retaining ring to the disposal drain at the underside of the sink bowl. Twist the retaining ring clockwise until it is hand tight. Snug the retaining ring by placing the edge of the screwdriver on the notch on the retaining ring and tapping it until it is tight.
Connect the electrical wire to the power circuit in the kitchen. Run the wire to the toggle switch and the disposal unit according to the manufacturer's instructions for the type of toggle switch you are using. Screw wire nuts on the wire splices to prevent them from coming apart and to cover them. Push the wire ends into the disposal unit and install the cover on the wire box. Tighten the screw on the wire box using a screwdriver.
Place the disposal at the bottom of the disposal drain. Insert a screwdriver into the locking ring and turn the ring clockwise to lock the garbage disposal into place. Install the long end of the P-trap into the disposal unit. Tighten the retaining screws using a screwdriver. Connect the trap end to the drainpipe and tighten it using a pipe wrench. Turn the power back on to the kitchen at the breaker box.
Run water into the disposal drain. Flip up the toggle switch to turn on the garbage disposal to test the operation of the unit. Check the drainpipes around the disposal drain and the garbage disposal to be sure there are no leaks.