Install Sewer Tee
Examine the sewer pipe inlet located nearest the sink and washing machine. This is usually a free-standing pipe with an open end. If there is not a tee connection for the sink inlet, one will need to be installed.
Turn off the water supply for both the washing machine and the sink. Both of these fixtures will have two separate supply valves, one for the hot and one for cold water. Rotate the knobs on the ends of the valves clockwise all the way to cut off the water.
Unplug the washing machine from the power outlet.
Cut the sewer inlet pipe in half about halfway down. On metal pipe, use a rotary cutting tool with a metal cutting blade. Use a hacksaw or other saw on PVC pipe. Sand down any rough edges on the pipes.
Connect a tee fitting to the sewer pipe. Secure a metal tee to the pipe with a rubber coupling and hose clamps. Tighten the clamps with a screwdriver. Point the tee in the direction of the sink drainpipe. A PVC pipe can be glued into place with primer and PVC glue.
Connect a straight drainpipe piece to the top of the tee. Secure it with a rubber coupling on metal pipe or glue another PVC pipe in place. Secure the pipe to the nearest stud or wall with a clamp to keep it steady.
Connect the Sink and Washing Machine
Insert the drain hose from the washing machine into the top of the sewer pipe. Secure it in place with a plastic tie or hose clamp.
Fit together the p-trap and drainpipe and place them into position between the tailpiece and the sewer pipe. This will help you determine if the pipes need to be cut further before final placement. Cut PVC pipes with a hacksaw and metal pipes with a rotary tool with a metal cutting attachment. Sand down any rough edges.
Connect the drainpipe for the sink to the tee inlet. Glue PVC pipe in place with primer and glue. Secure metal pipe by applying pipe thread compound to the drainpipe before screwing it into the tee.
Insert the p-trap in place between the tailpiece on the underside of the sink and the drainpipe. Slip the couplings over the end connections and tighten them with a wrench.
Turn on the water supply valves for the sink and washing machine by rotating them counterclockwise.
Plug the washing machine back into the wall outlet.