Turn off the water to the RV and completely drain the pipes in the corresponding area where you will be working. Shut the pump off at the shut-off valve, or if you are at an RV hookup, disconnect the supply line or turn the water off at the faucet. Turn on all faucets in the RV to relieve pressure on the lines and help the affected area drain.
Purchase enough replacement pipe and couplers to fix the area. Existing plumbing will be labeled with size and type; but if you want to be completely sure of the size, you can take the old plumbing into your local home improvement store and order exactly the parts you need to replace after you remove them.
Remove the damaged section of pipe and cut any new pieces to fit. Use a hacksaw or PVC cutter to cut the pipes and clean the burrs out of the ends of the cuts by giving the edge a quick scrape with a screwdriver. Dry-fit the couplers to ensure everything fits before you prime and glue the pieces together.
Splice the old plumbing into the new plumbing. Apply primer to the inside of each coupler and the outside of each piece that will slide into a coupler, coating the entire contact area. Once it is primed, apply the pipe cement and ensure it coats the entire primed area.
Slide the pieces together and hold them in place for a couple of minutes. Repeat the cutting, cleaning, priming and cementing process for all the couplers and pieces of pipe that need to be replaced.
Wait at least 24 hours for everything to dry then slowly return pressure to the water pipes in your RV. Run all of the taps for several minutes after you restore water pressure and check for leaks in the pipes you just replaced.