Strip the two ends of the wires you want to splice together. This will involve stripping the outer insulation, then the shield layer, then the inner insulation from the bare wires.
Twist the two wire ends together firmly. Try to get the spliced wires to go together as straight as possible.
Apply electrical tape or shrink tape to the bare wires, making sure to overlap with the original insulation to cover any bare wire completely.
Apply wire mesh tape to the spliced area. It should overlap with the outermost layer of insulation on either side of the gap.
Wrap the entire length of the wire mesh tape in electrical tape, so that it is well overlapped on either side.