Shut off the valves that lead to the leaking pipe then wipe it down with an emery cloth. Wipe the pipe down again with a dry rag to remove any dust left over from the emery. The pipe needs to be completely clean for the repair to properly bond with the brass.
Apply flux over the damaged section of pipe. Wear protective gloves and follow all instructions on the packaging for best results because flux is corrosive and can be dangerous if misused. Flux removes contaminants from the pipe when heated.
Heat the pipe with a propane torch so that the flux reacts with the brass. Wear a safety visor and long-sleeved clothing to help prevent injury. The flux will bubble and start to drip when it reacts to the brass, which only takes a few seconds.
Place a lead-free soldering wire over the leaking area of the pipe on the opposite side from the torch. The pipe should be hot enough that the wire melts on contact and spreads out over the damaged area. Wipe away any excess with a rag. It is still hot so keep your gloves on. Allow the solder to cool. As it does, it seals off the leak. Wipe down the pipe with a rag once the solder hardens.
Install a dehumidifier in the room where the pipe is to lower the ambient air moisture. This helps eliminate pipe sweating problems. Ventilate the room regularly as well, if possible, to help keep the pipe dry.
Place an insulating sleeve over the pipe to further protect it against sweating problems.