Download the schematic from the download page. Look at it and place all the pieces before soldering anything! Place the 8-DIP opamp first, about center, then place the FET, on the perimeter so that the heat sink will press against the housing, then place all the resistors. Remember that the 0.1 ohm resistor must be precise in value and 1/2W or 1W (at least) otherwise known as a 'sense resistor.' In the pictures, the white ceramic tablet is the resistor, and the metal sheet is the heatsink for the FET.
Preferably, the potentiometer and on/off switch should be in the same package. Make sure the pot is linear taper, not log/audio taper.
Use solid-core wire when making jumper-wires on the board, and stranded for wires that go to the pot/switch/lamp.
The other side of the circuit board, showing the heat sink, and the large sense resistor. Also, the lamp socket is visible in the top lefthand corner.
To connect to the lamp, you can either (carefully) solder directly, or get a socket. The lamp should last a really really long time (1,000hrs at least) so there's nothing particularly wrong with connecting directly to the lamp. Just make sure you can still assemble it (read the housing assembly instructions since a ring needs to go between the board and lamp).
I didn't include a fuse, but you may want to. (A proper LiIon battery is current limited anyways, which is why the whole system is current-controlled.)
Use heat-shrink liberally when necessary, not electrical tape. Electrical tape doesn't hold as well.
Plug in the lamp and give power to the system, verify that it works, there should be a ~150mV drop across the resistor, and a voltage that is 32 times that on pin 7 of the op amp. There should be 5V at pin 2. Turning the pot should dim/brighten the lamp. (Hopefully)