Three-pin microphone cables, or XLR cables, are the typical way microphones are connected to PA and recording equipment. XLR cables are wired in balanced configuration, which allows for natural noise-cancelling tendencies over long lengths of cable. Wiring any device that uses XLR connectors is straightforward, as pins are numbered and wired in a standard manner.
Identify the pins of the XLR connector with which you are working. Three pins are arranged in an inverted triangle. The bottom pin is always Pin 3, the negative or "cold" pin. The upper two pins are Pin 1, which is the ground connection, and Pin 2, the positive or "hot" pin. Their left/right orientation will change from front to back of a connector, and from male to female connector. Most XLR plugs have the numbers moulded into the base.
Locate the hot and cold wires. There is no standard convention for colour of wires. If you are replacing the XLR male connector on a microphone, there may be an indication of positive or negative on a circuit board. If you are in doubt, refer to microphone schematics or a trained technician. If you are wiring both ends of a cable, choose which wire to use as hot and cold. The shield around the inner wires will be your ground connection, going to Pin 1. Use a multi meter to determine which wire is which if you are replacing only one end. In a microphone, connect Pin 1 to the chassis of the microphone, or other common ground point.
Place connector housings on cables prior to soldering. Tin the ends of each wire to be soldered with a small amount of fresh solder to aid good connection. Solder each wire to its appropriate pin base using as little contact with the soldering iron as possible to assure good flow of solder while avoiding overheating of surrounding parts. Check the finished joint for solder bridges and other flaws. Cover the connector with its housing, tightening strain reliefs with the small screwdriver. Check pins for continuity with the multimeter.