Plastic PVC pipe and fittings are inexpensive and easy to install. However, do not take this work lightly. Once glued together a joint is rock-hard and cannot be adjusted. If you make a mistake, you'll have to cut out the section and start over.
Making a dry run
To prevent a mistake, cut and assemble the pipes in a dry run: Cut and temporarily join five or six pipes and fittings and make sure that the last pipe in the run is facing the right direction. Use a felt-tip pen to make alignment marks on all the joints where the fitting must face correctly. Disassemble, keeping careful track of the order of installation. Apply primer to each pipe end and each fitting. Apply cement and join each pipe in order.
About an hour to cut and assemble five or six pipes and fittings
Felt-tip marker, PVC saw or backsaw and miter box or power miter saw, deburring tool
Sawing, measuring, working methodically
Make a drawing of the drain/vent assembly; clear a path for the pipes
Primer and cement for your type and size of pipe
When measuring allow for the distance the pipe will travel inside the fitting. Use a felt-tip marker to mark the pipe. You can use a hacksaw or backsaw to cut PVC, but a plastic-pipe saw is easier to use. A power miter saw with a fine-cutting blade is easiest of all. Cut it square.
Apply primer to the inside of the fitting openings and to the pipe ends. The applicator should be wet enough to produce a fairly dark line but not so wet that the primer drips. Place the pieces where they will not get dirty. If debris sticks to the primer, it will be difficult to join the pipes.
Push the pipe into the fitting and twist so the alignment marks line up. Hold for a few seconds, then wipe with a damp cloth. In a minute the joint will be strong enough so you can assemble the next piece. After 15 minutes you can run unpressurized wastewater through the pipes.