Trace the wires to their points of origin and identify which is which. There will always be a ground wire, usually colored black, and at least one live wire. The live wire will be red or white.
Strip approximately 1 centimeter of insulation from each of the wires using the wire strippers. Take care not to cut through any of the internal fibers. Twist the strands of the wire together, to make a neat single strand. Ensure that nothing is touching the tip of the soldering iron, and plug it in. Wait a few minutes for the iron to heat up.
Melt 3-5 millimeters of solder onto the tip of the iron and touch it to the bare section of the negative ground wire, the black one. Hold the wire to the ring-shaped contact at the mouth of the output jack. Take the iron away and allow the solder to cool. Check that the connection is solid and immobile. Solder the positive live wire to the extended "tip" connection of the output jack.
Remove the locking nut from the thread at the end of output jack. Push the threaded section of the output jack through the chassis of the device, so the threads are protruding outside. Screw the locking nut onto the threads, holding the jack in place so it doesn't rotate as you tighten the nut. Tighten it with the wrench and test the jack.