The Joule Thief part of the circuit requires a small hand-wound toroidal transformer that we will make and add in this step.
I'm using ferrite beads around 9.8mm wide by 7.5mm deep with an 6.5mm diameter hole. Whatever the size you use, you'll want enough wire for 6-8 turns. For beads the size of mine, take about 20-30 cm of a pair of insulated 22-gauge solid copper wire (I use wire from an old 3-pair telephone cable). Contrasting colours make life easier. Push the wires through your torus leaving around an inch (2.5 cm) sticking out at one end. Now loop the long ends round until you have made 6-8 loops spread evenly round your bead. My beads are pretty much full after 8 turns of this wire.
I have made a few joule thieves and in my experience the ferrite bead is the most likely part to cause a problem. Some types of beads work and some don't and I have not yet divised a way to tell before trying them.
Cut down the leads to an inch at most (say 2cm-ish) and strip the ends. At this point it's handy to use a small sticky-pad to hold the torus in place.
Now take a wire of one colour from one end of the torus and the other colour from the other end and put them into holes 1 and 2. The other ends go into holes 3 and 4 so that the hole in the torus now points across the board. It should fall naturally so that the wires connect from holes 1 to 4 and 2 to 3, but check or it won't work! Bend the wires out a little to hold them, turn the board over and solder it.