Begin by completely clearing out the cabinet under the sink to create ample workspace. Place a bucket directly under the P-trap and garbage disposal. Lay down several old towels around the bucket to absorb any spills. The most critical safety step is to disconnect the power to the disposal. Locate the power cord and unplug it from the wall outlet. If your unit is hardwired, go to your home's main electrical panel and switch off the circuit breaker that controls the garbage disposal. To be certain, use a non-contact voltage tester to verify that there is no electrical current flowing to the unit before proceeding.

First, locate the flexible, ribbed dishwasher drain hose connected to the large inlet nipple on the side of the garbage disposal. Use a flathead screwdriver or a 5/16" nut driver to loosen the metal hose clamp securing it. Wiggle the hose off the nipple and immediately direct the open end into your bucket to drain any water. Next, identify the large slip nuts that connect the P-trap assembly to the disposal's discharge tube and the drainpipe coming from the wall. Using a pair of channel-lock pliers, turn these nuts counter-clockwise to loosen them. They may be tight initially. Once broken loose, you should be able to finish unscrewing them by hand. Carefully lower the P-trap, emptying its water content into the bucket.

The garbage disposal unit is heavy and will drop once released. Support its weight from below with one hand, or place a few blocks of wood or a small stool underneath it for support. Locate the mounting ring at the top of the disposal where it connects to the sink flange. You will see several small lugs on this ring. Insert the tip of a large flathead screwdriver or the special 'Jam-Buster' wrench (if you have it) into one of these lugs. Apply firm pressure and turn the entire mounting ring counter-clockwise about one-quarter turn. You will feel it unlock from the mounting assembly. Once unlocked, carefully lower the heavy disposal unit and move it out from under the sink.

From underneath the sink, locate the three screws on the remaining mounting assembly. Loosen these screws until the lower part of the mount (the backup flange) can be removed. Next, you will see a thin, springy metal snap ring holding the rest of the assembly in place. Carefully pry one end of this snap ring out of its groove using a flathead screwdriver. Be cautious as it can spring off unexpectedly. Once the snap ring is off, the rest of the mounting hardware will come free. Move to the top of the sink. Use a putty knife to gently pry up and remove the old sink flange (the metal drain piece). Scrape away all the old, hardened plumber's putty from the sink's surface. For a perfectly clean surface, wipe the area around the drain hole with a cloth and a small amount of rubbing alcohol.

Take a generous amount of fresh plumber's putty and knead it in your hands to warm it up. Roll it into a uniform, snake-like rope about 1/4-inch thick. Wrap this putty rope around the underside of the new basket strainer's flange. From above the sink, press the strainer firmly down into the clean drain hole. The putty should squeeze out evenly around the entire perimeter. From underneath the sink, slide the rubber gasket up against the sink bottom, followed by the fiber or cardboard friction washer, and finally the large metal locknut. Hand-tighten the locknut as much as possible. To finish, use channel-lock pliers or a dedicated strainer locknut wrench to give the locknut a final half-turn. To prevent the strainer from spinning while you tighten, have a helper hold it steady from above by inserting the handles of pliers or a screwdriver into the crossbars. Wipe away the excess putty that squeezed out on the top side of the sink with your finger or a cloth.

Begin by attaching a flanged tailpiece to the bottom of the newly installed basket strainer, securing it with a slip nut and washer. Now, loosely assemble the rest of the pipes to 'dry fit' them. Connect the second tailpiece from the other sink bowl. Attach the continuous waste tee (or sanitary tee) to connect both tailpieces. The outlet of the tee should point toward the drain pipe in the wall. This tee fitting must have a baffled side inlet for the dishwasher hose. Attach the dishwasher drain hose to this baffled inlet and secure it with its hose clamp. Create a 'high loop' by fastening the dishwasher hose as high as possible inside the sink cabinet before it connects to the tee. Finally, connect the P-trap between the bottom of the waste tee and the drainpipe in the wall. You may need to use a hacksaw or tubing cutter to trim a tailpiece or the horizontal arm of the trap for a perfect fit. Once you confirm everything aligns correctly and slopes gently downhill towards the wall drain, hand-tighten all slip nuts, then give each a final quarter-turn with channel-lock pliers. Do not overtighten.

Ensure your bucket is still positioned under the P-trap. Place the stoppers in both sink drains and fill both bowls about halfway with water. While the sinks are filling, visually inspect all your new connections. Once filled, remove both stoppers simultaneously to send a large volume of water through the new drain system, which puts the joints under pressure. As the water drains, meticulously check every connection point for any signs of moisture. Run a dry paper towel under each slip nut and joint, as this will make even the smallest drip immediately visible. If you find a leak, the most common cause is a misaligned slip washer or a nut that isn't tight enough. Try tightening the leaking nut slightly. If the leak persists, disassemble that specific joint, ensure the washer is seated flat and correctly, and then reassemble and re-tighten.