I used the joule thief in its simplest form, as probably published November 1999 issue of EPE (Everyday Practical Electronics). It's a NPN transistor, one resistor, a bifilar transformer and a LED (any color). I found the diagram on the web and worked immediately.
How did I wind the transformer? I saw many questions about it around the web. First of all, you need some luck since you're probably winding it on a core with unknown characteristics. I took some length of enameled copper wire (2 metres), bent in half and wound about 8 turns through the core. Windings are spread about on 80% of the core. The core is a ferrite bead recovered from WhoKnowsWhereLand. Try it first with a fresh battery. If it doesn't lit, add some turns and try again. If at 20 turns you still don't get light, then:
- check your LED is wired properly
- change the core
Before someone asks, no, I have no spare cores to send around.
With the saline battery my joule thief produced noticeable light (in darkness) for 36 uninterrupted hours. I will measure how much current it draws at the next battery change.