Remove everything from under the sink so you have easier access to the plumbing. Familiarize yourself with the pieces of the plumbing. The piece that extends from the bottom of the sink is the downpipe. The piece that slides over the downpipe and looks like an S or a P is the sink trap. The pipe that the trap slides over and secures to is the sewer drainpipe.
Loosen the compression nuts at the top and bottom of the trap. In most cases, you can use your hand to loose the compression nuts, otherwise you must use a pipe wrench.
Slide the trap down onto the sewer drainpipe to remove it from the downpipe. Tilt the trap to the side slightly and slide the trap upward to remove it from the sewer drainpipe.
Slide the waste tee pipe onto the sink's downpipe and push it up as far as it will go. Lightly tighten the compression nut on the top of the waste tee pipe. Do not tighten down hard as you will likely need to reposition the pipe before your task is complete.
Slide the trap onto the sewer drainpipe and slide it down as far as you can. Position the top end of the trap directly under the waste tee pipe and then try to slide the trap onto the pipe. If the trap fits, tighten the compression nuts on each end of the trap and on the top of the waste tee pipe. If the trap does not fit, remove the waste tee pipe and trim off the necessary amount from the bottom of the waste tee pipe using a hacksaw. After cutting off enough to allow the trap to fit, secure everything together.
Secure the drain hose supplied with the dishwasher installation kit onto the tee using the supplied band clamp and a screwdriver.
Extend the hose through the side of the cabinet and into the area under the counter where you will install your dishwasher. If necessary, drill a 2-inch hole in the side of the cabinet using a hole saw and a hand drill.
Locate the discharge pump on the dishwasher. In most cases, you will locate an access hole on the back of the dishwasher at the bottom. Secure the drain hose to the discharge pump by sliding the couplers together. Tighten the band clamp that holds the couplers together using a screwdriver.