When a leak in a copper pipe develops, it's location will be obvious. You will not have to go looking for it; it will be dripping on you. It is not widely known but copper pipe will corrode over time and start to leak all by itself.
Shut the water off. If the valve cannot be located you can turn the water off at the water meter out at the street in front of the house.
Purchase a compression fitting the size of the pipe you are repairing. The compression fittings consist of a main body, nuts and ferrules.
Drain the pipes and cut the pipe in convenient spots so that you remove the portion that is leaking. Be sure to leave enough pipe protruding so you can get the nut and ferrule from the compression fitting onto the pipe. If you have a pipe cutter this job is a snap. If you don't have a pipe cutter you can use a hacksaw.
Clean the remaining pipe with sand paper where the compression ferrules are to be placed. Cut a new piece of pipe from extra pipe to fill in what was cut away.
Connect the ferrules, nuts and body. Tighten the nuts. These nuts need to be very tight. Turn the water back on. If little leaks develop just tighten the nuts up some more until the leaking stops.