Drain and vent lines must be positioned precisely, so you should install them before the supply pipes. It may be possible to simplify supply runs by moving a vent pipe over a few inches.
If you must run drainpipes across a floor, carefully calculate the amount of vertical space available; you must slope the drainpipe at 1/8 to 1/4 inch drop per foot.
Sometimes it's difficult to visualize how drainpipes will travel through walls and floors. Once you start assembling the pieces and testing them for fit, you may need to modify your plans.
Some inspectors prefer horizontal vent pipes to be sloped so condensation can run back to the drainpipes; others don't consider this important. To be on the safe side, slope the vents.
Working with a helper, about two days
PVC saw or power saw, level, carpentry tools
Cutting and joining PVC pipe, running pipes through walls, connecting new pipe to old
Have your plans approved by an inspector; prepare the room
PVC pipe and fittings to meet codes, PVC primer and cement, pipe strap, fitting to join to existing drainpipe
Start with a length of 3-inch pipe long enough to reach the basement or crawlspace. You may be able to cut it to exact length after it has been installed. Dry-fit a Y-fitting, a length of pipe, and a low-heel vent fitting as shown, aligning them precisely.
Insert the assembly down through the wall plates and temporarily anchor it. Make sure the Y-fitting is low enough to allow for installation of the other drain lines. Once you are sure of the configuration, pull up the assembly and prime and glue the pieces.
Dry-fit a length of 3-inch pipe and a 4x3 reducing closet bend to the low-heel fitting. Check that the center of the closet bend hole is the correct distance from the wall -- in most cases 12-1/2 inches from the framing to allow for 1/2-inch drywall. Check that the pipe slopes 1/8 to 1/4 inch down to the fitting. (If necessary you can trim the top of the closet bend after the flooring has been replaced.) Once you are sure the toilet drain setup is correct, mark the alignment of the fittings and disassemble. Prime and glue the pieces. Support the closet bend with a strap.
Run a horizontal pipe to the existing pipe and assemble the parts needed for tying into it. All fittings should be Ys or drain elbows so wastewater can flow easily. Hold the horizontal pipe so it's sloped at 1/8 to 1/4 inch per foot and mark the existing pipe for cutting.
If the existing pipe is cast-iron, take care to support it securely before cutting. In the setup shown, a 4x3 Y connects to the house drain using no-hub fittings (which should be used to connect to either cast iron or ABS). Once you are sure the fittings are correct and the horizontal pipe slopes correctly, make alignment marks. Disassemble the parts, apply primer and glue, and reassemble the pieces in order, starting at the existing drain.
Slip lengths of 2-inch pipe down through the holes drilled in the floor plate for the tub and sink vents. Have a helper hold the pipes plumb as you mark the plate below for notching. Cut notches about an inch wider than the pipe to accommodate a fitting.
Cut and dry-fit the horizontal drainpipe and the fittings for connecting the tub and the sink drains. (A 3-inch horizontal pipe is shown, but your inspector may permit a 2-inch pipe.) Insert a street elbow into the Y and hold the other pieces in place to mark for cutting. Make sure the horizontal pipe slopes at a rate of 1/8 to 1/4 inch per running foot. Install a reducing tee and a 45-degree elbow (or street elbow if you need to save room) for both joints. If the pipe will be accessible, install a cleanout on the fitting for the tub; otherwise install a drain elbow instead of a tee.
To plumb the drain for the tub, dry-fit a 2-inch trap onto a length of 2-inch pipe that is longer than it needs to be. Study the directions for the tub to determine precisely where the trap should be located. Hold the trap-and-pipe assembly in place and mark it for a cut. Dry-fit and check that the horizontal pipe slopes correctly. Once all the parts are accurately assembled, draw alignment marks and prime and glue the pieces together.
Your codes may require the horizontal revent lines be as high as 54 inches above the finished floor, or at least 6 inches above the fixture flood level (the point where water will start to spill out). Use a carpenter's level to mark the studs for drilling holes. Run the horizontal vent lines sloped downward toward the fixtures at a rate of 1/8 to 1/4 inch per running foot. Drill holes, cut pipes, and connect them in a dry run using drain fittings.
Install a sanitary tee facing into the room for the sink trap. The ideal height is usually 18 inches above the finished floor, but check your sink instructions to be sure. Cement a 1-1/4-inch trap adapter into the tee. Install a piece of 1x6 blocking and anchor the pipe with a strap.
Run the new vent line over to the tee fitting. The pipes should slope gently away from the existing vent pipe so water can travel downward. Your inspector may want you to include a tee fitting to be used for testing: Once the drain system is assembled and cemented, plug the drainpipe at the lower end. Pour water into it until all the drain and vent pipes are filled with water. Allow the water to sit for a day to make sure there are no leaks.
If the toilet drain does not connect directly to a vent, you must find another way to vent it. If the drain line runs away from the wall where you want the vent, use a reducing Y and a 45-degree street elbow to point the vent line toward the wall. The horizontal vent pipe runs right next to the closet bend.