If you have decided not to use a dimmer, you'll just have to solder the positive wire coming from the power supply to the switch, another wire from the switch to the LED's positive and the power supply's negative to the negative of the LED's.

If you have decided to use the dimmer circuit provided in this instructable, the positive wire will also be soldered to the switch, but a wire must be soldered from the switch to the circuit's VCC, as indicated in the schematic (Step 10). The LED's positive wire will be connected to LED+, and its negative to LED-, which is the drain of the MOSFET transistor. The negative or GND will be connected to the negative wire coming from the power supply.

The 47k potentiometer middle lead must be connected to pin 7 on the 555, the lateral leads are connected to the diodes, it doesn't matters which way around, connecting them one way or the other will just change the direction in which you have to turn the potentiometer in order to increase or decrease the brightness.

To wire the lamp I used some wires I had laying around, I cut one meter of them and with the help of a drill I twisted them to make them look neater, I coiled the already coiled wires around a rod and installed them on the lamp, connecting the LEDs to the circuit. The double coil allows the wire to extend when the arms are extended too. A couple of screws are all what's needed to keep the wire attached to the arm of the lamp.

The holes for the switch and the potentiometer are drilled, and the wires are passed through a small recess at the bottom, the circuit board is secured in place with some glue. The switch and potentiometer are installed and soldered in place. For the switch, I used a file to carve the rectangular shape to make it fit.

For the PSU I'll use a 12 volt, 2 amp wall wart. Always check the amperage of the wall wart is higher than the amperage you'll be needing.