First, determine the exact location and dimensions of your new vanity. Obtain the manufacturer's specification sheet or measure the vanity directly. Mark the center of the vanity on the floor and transfer this mark up the wall using a level. From this centerline, mark the standard heights: the drainpipe center should be between 16-20 inches from the finished floor. The hot and cold water supply lines should be 3-4 inches above the drain, and spaced 4-6 inches apart on either side of the drain centerline. The hot water supply (left) and cold water supply (right) should be clearly marked.

Locate the main water shutoff valve for the house and turn it completely off. Open the lowest faucet in the house (like a basement or outdoor spigot) and the highest faucet to drain all remaining water from the supply lines. This prevents water from spilling when you cut into the existing pipes. If you are tying into an existing drain stack, ensure no water is being run from fixtures above.

The vanity drain needs to connect to the home's main Drain-Waste-Vent (DWV) system. Using a drill with a 2-inch hole saw or auger bit, drill holes through the center of the studs leading from the vanity location to the main vertical drain stack. The holes must be pitched downwards towards the main stack at a rate of 1/4 inch per foot to ensure proper drainage. Use a level to verify the slope. Cut sections of 1.5-inch PVC pipe to run through the studs. You will need to cut into the main stack to install a new sanitary tee fitting that will accept the new vanity drain line. Dry fit all pieces first. Then, apply PVC primer to both the pipe end and the inside of the fitting, followed immediately by PVC cement, and firmly push the pipe into the fitting with a slight twist. Hold for 30 seconds.

At the vanity location, install a 1.5-inch PVC 90-degree elbow onto the drain arm inside the wall. Cut a short piece of 1.5-inch PVC pipe (the stub-out) long enough to extend about 4-6 inches past where the finished wall will be. Use primer and cement to glue this stub-out into the elbow. Finally, place a temporary test cap on the end of the stub-out to prevent debris and sewer gas from entering the room.

Using a drill and a 3/4-inch bit, drill holes through the studs from your hot and cold water main lines to the marked locations for the vanity supplies. Run a red 1/2-inch PEX tube for the hot supply and a blue 1/2-inch PEX tube for the cold supply through these holes. Leave several extra feet of tubing at both ends for flexibility. Secure the PEX tubing to the studs every 16-24 inches using PEX clamps or talons to prevent movement and noise.

Install a piece of 2x6 or 2x8 lumber horizontally between the studs at the height of your water supply marks. This is called backing and provides a solid mounting point. Secure two 1/2-inch PEX drop-ear elbows to the backing with wood screws at your marked locations. Cut the PEX tubing to length and connect them to the elbows using a PEX crimp tool and stainless steel crimp rings. Slide a crimp ring over the pipe, insert the pipe into the fitting, position the ring 1/8 to 1/4 inch from the end of the pipe, and compress it with the crimp tool until it clicks. Finally, wrap the threads of the drop-ear elbows with Teflon tape and screw on the 1/4-turn angle stops (shutoff valves) until they are hand-tight plus a quarter turn with a wrench.

With the drain capped and the new angle stops in the closed position, you can now test for leaks. Go back to the main water shutoff valve and turn it on slowly to allow the pipes to fill gradually, which prevents water hammer. Return to the bathroom and carefully inspect all the new PEX connections and the threaded connections at the angle stops. Look and feel for any signs of moisture. For a more thorough test required by some codes, you can attach a pressure test gauge to one of the angle stops or an outdoor spigot and pressurize the system to check for any pressure drop over time.

Once you have confirmed there are no leaks, the final step is to protect your new plumbing. Install steel nail plates on the front edge of any stud where water or drain pipes pass through. These plates are hammered into the wood and will prevent future drywall screws or nails from accidentally puncturing your pipes. Your rough-in is now complete and the wall is ready for insulation and drywall.