Place a bucket below the P-trap underneath the sink. Unscrew the couplings on either end of the trap with pliers. Slide the P-trap out of the plumbing and empty the water inside into the sink.
Unscrew the jamb nut on the underside of the sink with a pair of channel-lock pliers. Slide the jamb nut and the washers beneath it off the straight tail piece. Unscrew the tail piece by turning it counterclockwise.
Hit the underside of the sink drain with a rubber mallet to knock it out into the sink above. Remove the old drain.
Clean up the area around the drain in the sink, using a putty knife. Remove any old caulk or putty.
Apply a bead of plumber's putty around the drain opening. Secure the drain top from the disposal. Secure the drain top from underneath the bottom of the drain and tighten it according to the manufacturer's instructions.
Lift the disposal up and insert it into the disposal ring. Either turn it to lock it in place, or tighten it in place with the included disposal screwdriver or a Phillips screwdriver.
Plug the disposal into the under-sink outlet. For a hard-wired installation, remove the plate on the underside of the disposal. Connect the wires from the home circuit to the terminals on the disposal --- the black wire connects to the hot terminal, white connects to the neutral and bare copper goes to the green terminal. Some disposals may have wires on the terminals preinstalled. In this case, the wires from the home electrical system simply need to be connected to the disposal wires with wire nuts and electrical tape. Gently press the wires into the disposal case and replace the electrical plate.
Connect the drain plumbing for the disposal.
Connect the dishwasher hose, if present, to the disposal. Trim off the end of the disposal hose to the proper size for fitting over the dishwasher nipple. Secure it with a hose clamp.
Turn on the power for the disposal. Run water in the sink and switch on the disposal. Check for leaks.