How to Plumb a Bathroom
Before plumbing your bathroom, you'll want to determine where the tub, sink, and toilet will be. Make sure to take measurements and factor in how much space there will be between each feature. Then, you'll need to drill holes in the appropriate places so you can run pipes to the fixtures. Once you've installed the hot, cold, and drain pipes, you can connect the sink, toilet, and tub faucet to them and secure the fixtures to the floor or wall.
Determine the placement of the bathroom plumbing fixtures. You will need to figure out the placement of your bathtub or shower, sink and toilet. This will determine where you will need to run the plumbing lines. You will have to cut holes in the floor so that you can run the pipes to the fixtures, so determining the exact placement is important. Locate and carefully mark all cut points and drill points Measure again to make sure your markings are accurate. "Measure twice, cut once" may be an old saw, but it still has teeth. Do all the cutting and drilling necessary. You want to do the prep work before you turn off the water, to minimize your "dry" time. Turn off the water to the house. Before doing any work on your plumbing, you will need to turn off the bathroom water lines. Locate the water valves and turn them off. Install the water lines. You will need to run 5 water lines into a standard bathroom: a hot and cold line for both the bathtub/shower and the sink, and a cold water line for the toilet. You can either run these lines through the wall or up from the floor, depending on the location of your bathroom. Attach flexible lines from the hot and cold waters line to the sink and bathtub faucets. Using sandpaper, clean the copper pipes to make them smooth, and then solder the lines to the main water line. Connect the drain lines. For your bathroom, you will need multiple sizes of drain lines. The drain line for the toilet should be either a 3 inch (7.62 cm) or 4 inch (10.16 cm) line. After you attach the pipe to the toilet drain, the pipe should slope downwards toward the main drain line. The sink drain line will be 1.5 inches (3.81 cm) and the bathtub will use a 2 inch (5.08 cm) drain line. Set the toilet in place. Toilets usually come in 2 pieces: a tank and a bowl. Start by installing the bowl. Connect the closet flange from the waste pipe to your toilet. To do so, glue the closet flange into place so that the slots line up with the toilet's bolt holes. Set the bowl over the bolts and on the flange. You may want to sit on the toilet and rock back and forth a bit to get it on correctly. Check if the bowl is level, and then tighten the nuts and the washers of the closet bolts. Attach the toilet's tank to the bowl using nuts. Connect the water line and then caulk around the base of the bowl to secure the toilet. Install the sink. Start by positioning the stand to do a test fit. Mark where the floor bolt should go and drill a hole through the sink stand and fasten it to floor using a nut and bolt. Connect the sink to the hot and cold water lines. Also connect the handles, stopper and drain to the top portion of the sink. Set the sink onto the stand and glue an adapter with threads to the drain pipe. Hook up a tub and shower unit. Mark the outline of the tub on the floor so that you can estimate where the drain will be. Run the drain line and dry fit it. Once you have it lined up, glue the waste line to connect to the tub's drain. Set the tub and check that it is level. Use a plunger on your toilet if it should get clogged. Once the plumbing in your bathroom is complete, you may still run into problems in the future. To unclog a toilet, press a plunger against the hole and push the plunger up and down. If that does not work, you can use a closet auger, which has a coil at the end that goes into the toilet, and a handle at the other end which makes the coil go deeper into the pipes. Unclog the sink using a plunger or an auger. If your sink clogs, you can use the plunger or with an auger. You can also clean out the trap under the sink by removing the cover to the trap. It will be located at the bottom of the pipe right before it enters the wall. Stick a hanger or a wire through the trap to see if you can pull anything out. If that does not work, disconnect the pipe using a wrench and clean it out using detergent. Use a hose for the floor drain. Remove the strainer for the floor drain and push the hose into it as far down as it will go. Stuff rags around the hose at the drain entrance to close up the hole. Turn the water on at full force and then turn it off again. Continue turning it on and off until the water flows freely through it. Clear the bathtub drain using an auger. For the bathtub drain, unscrew the overflow plate and lift it out. Run the coil for the auger through the pipe to unclog the drain. 
Determine the placement of the bathroom plumbing fixtures. Turn off the water to the house. Install the water lines. Connect the drain lines. Set the toilet in place. Install the sink. Hook up a tub and shower unit. Use a plunger on your toilet if it should get clogged. Unclog the sink using a plunger or an auger. Use a hose for the floor drain. Clear the bathtub drain using an auger. 