You need a 25 to 30-watt soldering iron and soldering wire. Make sure not to breathe in the smoke generated by soldering. It is advisable to work in a well-ventilated room or near an open window when soldering.
The simplest circuit would consist of just a pickup and an output jack. Wiring couldn't be simpler: Solder one of the two pickup wires to the short lug and the other wire to the other lug. Plug in your amp and start to play. In this case you will have to adjust the volume at the amp.
If you wish to be able to do this directly on the guitar, a volume pot is required. Cut off about two inches of each pickup wire and strip the insulation off the ends over 1/8" (3mm). Look at the back so that its three lugs point to you. Solder one of the pickup wires to the left potentiometer lug. Soldering the joint should be done by heating for approximately three seconds and applying solder for two seconds (count in your head: "21,22,23" and "24,25"). Then leave the joint to cool for half a minute. If heat is applied for too long, the pot may be destroyed. A good solder joint is shiny; if its grey and ball-shaped, you have applied too little heat. In that case, re-heat the joint and apply a small amount of additional solder after a couple of seconds.
Use one of the above-mentioned cut-off wires to connect the potentiometer lug in the middle to the longer one of the two output jack lugs. Take the remaining of the cut-off wires and solder one of its ends to the shorter jack lug. Connect the other end, together with the remaining pickup wire, to the right potentiometer lug. It is advisable to use the potentiometer case as a shield against ambient noise. For this you need to bend the right potentiometer lug back until it touches the case of the pot. Heat the connection thoroughly and apply solder. This connection is more difficult to make because the larger surface of the pot case draws the heat until it is evenly heated. Again, remember that you can destroy the pot by heating it for too long: it has a thin conductive layer inside, which can melt. For making this joint, limit soldering to a maximum of 10 seconds with a 30 watts iron. Instead of bending the lug you can also use a short wire to connect the lug and the case.