Shut off the power, if need be, to the device you are repairing the wiring on.
Isolate the section of wiring that needs to be soldered. Use a wire stripper to remove approximately one inch of the rubber sheathing from the two ends of wire you will solder together. Clean the ends of the wire off with a rag.
Twist the two ends of wiring you will be soldering together with your fingers.
Plug in your soldering iron and allow it to heat up.
Place the tip of the soldering iron just beneath the joint. Touch the solder to the joint and allow it to melt over the joint. Do not move the wire until the solder completely cools.
Tear a small strip of electrical tape off and wrap it around the newly soldered joint on the wire.