Cut and remove a section of your existing waste pipe large enough to accommodate your waste Y-coupler. Measure the distance between the two ends of the Y-coupler and mark the existing waste pipe before cutting. Use a hacksaw or reciprocating saw to make the cuts as clean and straight as possible.
Cement the Y-coupler between the two ends of the cut pipe. Use a small amount of sandpaper to remove any rough spots on the ends of the waste pipe. Apply a liberal amount of PVC cement to both ends of the waste pipe and both female ends of the Y-coupler, as indicated by the PVC cement instructions. Fit the coupler between the two ends of the cut waste pipe so that the unattached end is pointing out away from the wall. When viewed from above, the coupler should look like a Y, and be oriented as it would be if it were laying flat on the floor. Cement the coupler in place and allow it to cure.
Attach your PVC 90-degree elbow to the remaining unattached end of the Y-coupler. Dry fit the elbow to ensure it fits properly. Orient the elbow so that it is directed downward. Once you are confident it will fit properly, cement it in place as you did the Y-coupler. Allow the cement to cure.
Attach your standpipe to the bottom of your downward-facing 90-degree elbow. The standpipe should fit so that its trap attaches to the elbow and the standpipe points straight up, running parallel to the studs in your wall. Cement the standpipe to the elbow and allow the cement to cure.
Secure the top of the standpipe to the wall or a stud using a pipe strap. Screw one end of the pipe strap in to the stud or wall next to the standpipe, wrap the pipe strap around the standpipe, and screw the other end in to the wall so that it holds the standpipe firmly in place. Give the standpipe two or three wiggles to make sure it is secured.
Attach your washing machine hose to the back of your washing machine, and feed a few inches of it in to your new standpipe. Standpipe hoses merely sit in place inside the standpipe, and are not clamped or secured. Test run the washing machine and check for leaks.