This may sound like a strange thing to learn how to do to anyone that has not had their bathroom or kitchen flooded by a broken water pipe, however I can assure the reader that they may at some point need to know how to do this. This will work with nearly any household materials (as hinted at in the required materials section,) and the procedure can be completed whether or not there is liquid running through the pipe at the time the work is completed.

Estimated time to completion: 1-5 minutes (with practice.)

Required Materials:
-15 to twenty feet or one roll of heavy twine, 2-5mm nylon cord or "550 cord" (parachute shroud line) can also be used.
-One neoprene sheet one to two square feet in size 5-10mm in thickness. (Heavy rubber gloves, flexible linoleum of the more pliable variety, densely woven fabric, black butyl rubber bicycle tubes, an old wetsuit or waterproofed canvas can also be used.) Note: For best results, keep several pieces of heavy neoprene around. This can be obtained from any local military surplus or diving equipment shop.
-One roll duct tape.
-One bucket.
-One waterproof flashlight.
-One roll heavy saran (plastic) wrap.
-One pair goggles.

Safety Note:
--If you are about to attempt to patch a pipe containing pressurized hazardous materials or flammable liquids it is strongly urged that you don all appropriate safety equipment as mandated by the MSDS (Material Safety Data Sheet.) MSDS peculiar to a specific workplace shall be stored in an open location as mandated by U.S. federal law and OSHA regulation. In the event that you believe that what you are about to do may threaten your life it is best to involve local authorities who have specific training to deal with these sorts of incidents. The procedures as noted below are designed to assist in a home/domestic setting, not to counter the initial effects of a major industrial accident.
--DO NOT USE THIS PROCEDURE FOR ANY FORM OF REPAIR ON NATURAL GAS PIPING. Natural gas coming into a home is a particularly toxic and dangerous substance, if a gas leak is suspected contact you local utility company immediately and evacuate the surrounding area.
--The first bit is meant for plumbing, other pipe problems are addressed below.

1. Don goggles and identify the discrepant piece of plumbing. If water can be secured prior to commencing work then do so, if not proceed directly to step two.
2. Examine damage. Apply patch such that it is centered over damage and clamp tightly with free hand.
3. Tightly tie free end of string around the center of the patch and directly over the top of the damage, such that it is wound in the same direction as the sealing material. In other words if one pulls on the string such that it rotates around the pipe, it will pull the patching material tighter vice looser.
4. Begin wrapping string around pipe as neatly as possible, keeping string taut and not allowing for any slack in the line. Try to keep wrappings as close together as possible, in other words when complete the wraps should appear as a "coating" of twine.
5. Continue wrapping down to the end of the patching material and continue for a distance of one inch past the end. Half of the patch should be secured at this point.
6. Commence wrapping in opposite direction, continuing to maintain all possible tension on line.
7. Terminate wrapping the patch with twine when one inch past the opposite end of the patching material.
Water flow at this point should have slowed to a near trickle or slight drip. If not patch was not wrapped tightly enough.
8. If water flow has ceased or slowed to a near trickle, tightly wrap patch to a distance of two inches past the end of the wrapping material with several layers of saran (plastic) wrap.
9. Wrap plastic coated patch in duct tape two inches past the end of the saran (plastic) wrap.
10. Congratulations, USS/HMS Kitchen should not sink at this point. In theory.
11. Place bucket beneath drip such that kitchen does not continue to flood and sink the house. Effect permanent replacement of damaged plumbing as soon as is practical.

Yurei learned how to do this courtesy of the United States Navy while in the Damage Control segment of Basic Training. It actually works, and if necessary (and you are close enough,) this can be demonstrated if you ask nicely.

AWW MAN! YOU LIKE BUSTED MY SHIT MAN! DAMN! And it really held the room together.
This is a little less serious than the above.
1. Find person responsible for damage to pipe. Commence to hassle individual.
2. Whine. Lots. You have fifteen minutes to complete this evolution.
3. Stare at ceiling.
4. Hassle individual again via phone.
5. Use duct tape. Fix pipe. More tape is better.
6. Using duct taped pipe as a material example of the strife caused in your life, hassle individual again.
7. Write vague and indecipherably bizarre daylog concerning damage to pipe, repair methods and hassling of discrepant individuals. Ensure references to characters no one has ever met are made to maximize effect. Quote Jean-Paul Sartre's Cookbook, the television will not be revolutionized and make obscure/foreboding references to 'The Man.'
8. Discover duct tape, when heated, becomes quite gooey.
9. Buy new pipe.

Yurei has no idea how well the above works, however from direct observation of his former roommates friends it appears to be a faithful and accurate duplication of actual used procedures.