Leaking copper pipe fittings are usually caused by a poorly soldered joint or an aged and worn-out joint that is no longer watertight. In either case, the joint must be opened again and resoldered to be sure the repair is watertight when completed. It is not as difficult as it may seem. Solder has a low melting point, and just has to be reheated. And reheating the joint may be all that is required to seal the joint completely without adding any extra solder. But it is always a good idea to add more solder to the joint, just to be sure.
Turn off the water valve supplying the leaking joint. This could be a small shut-off valve near the leaking joint, but it is more likely that the joint is controlled by the main water shut-off valve to the whole house.
Light a BernzOmatic torch with a striker, a match or a lighter, and begin heating the joint. When the joint is sufficiently hot, pull the water lines away from the leaky fitting. Immediately wipe the excess solder away from the ends of the pipes that the fitting were connected to while they are still hot. Discard the old fitting.
When the ends of the water lines have cooled, rub the ends with a piece of emory cloth. This will clean them and help the pipes accept soldering more readily. Brush a layer of flux onto the ends of the pipes, and place a new fitting over them. Unroll about 12 inches of solder so it will be ready when the pipe and fitting are hot. Begin heating the pipe ends, one at a time. When the fitting is sufficiently hot, the solder will immediately melt upon contact. Touch the solder to the edge of the fitting, and run the solder around the whole fitting. Repeat for the other pipes attached to the fitting.
Allow the repaired fitting to cool and then turn the water supply to the fitting back on to test for further leaking. The water will also finish cooling the fitting from inside the pipe so it will be safe to touch.
If the joint still leaks after the fitting has been replaced, repeat Steps 1-3. If the joint still leaks after several attempts, contact a licensed plumber in your area for additional help.
Keep in mind that the water lines and the fitting will be extremely hot and will burn you, if you do not use caution while handling and working with them. Leather work gloves will help keep you from getting burnt.