Copper is the preferred material for supply lines in most locales, although flexible or rigid plastic is permitted in some areas. Practice cutting copper pipe and sweating joints before you start.
Supply lines are usually routed so they do not cross drainpipes or vents. In most cases, it's easier to make the horizontal runs in the crawlspace or basement. Long runs and bends lower water pressure slightly.
Hammer arresters (Step 3) prevent banging noise when you turn off a faucet.
Copper pipe is easily punctured or dented, so position it out of harm's way and install nailing plates to the studs to protect pipes against errant nails.
Hot water is always on the left, cold water on the right.
About half a day to run supply lines for a sink and toilet
Drill, bit and bit extender, propane torch, fiber shield, tubing cutter, multiuse wire brush, groove-joint pliers, carpentry tools for installing braces
Accurate measuring and drilling, working with copper pipe
Install all or most of the drain and vent pipes; determine the supply routes
Copper pipe and fittings, flux, solder, damp rag
Consult the manufacturer's instructions to position pipes for the shower faucet, sink, and toilet. For example, the shower faucet in this plan calls for vertical pipes 10 inches apart. Use a spade bit attached to a bit extender to drill holes in the center of the wall plate if possible.
Tie into existing supply lines. Hot and cold stub outs are usually 8 to 10 inches apart and 19 to 23 inches above the floor; consult the manufacturer's instructions to be sure. A toilet stub out is usually 8 inches above the floor.
Dry-fit a complete assembly for the sink and the toilet. For each stub out, use a tee fitting, a 6-inch length of pipe (which you will cut off later), and a cap to protect the pipe. Install a hammer arrester to each.
Another option is to cut notches rather than holes and run supply pipes in front of the vent pipes. If you do this, be sure to install protective nailing plates, or else the pipes could be punctured by a nail when the drywall is installed.