The MakersBox has a great kit for beginners on Tindie:

Easy Joule Thief Soldering Kit

The perfect night-light, and a great way to learn how to solder.

The Joule Thief is a clever little circuit that can light a LED with a battery that is nearly dead. It does this with a pair of opposing magnetic fields. I like this circuit because it is simple to build, yet demonstrates some very complex electrical behavior.

I’ve designed a printed circuit board to help make this easier to build for beginning Makers. I used open source KiCAD software to lay it out (a future Instructable?), and OSHPark to manufacture it. If you want to just wire one up without the board, check out Angelo’s Instructable which uses essentially the same circuit.

The kit contains:

• 1 – PCB, https://oshpark.com/shared_projects/rLeF8F88
• 2 – AA Battery Clip, Keystone Electronics #92
• 1 – Ferrite Tubular Bead, Digi-Key 240-2301-ND or similar
• 1 – SPDT slide switch, E-Switch EG1218
• 1 – 1K resistor 1/8 – 1/4 W
• 1 – PN2222 Resistor, Fairchild Semiconductor PN2222ATA
• 2 nanoseconds (about 24″) of insulated wire. Two different colors are helpful.
• 1 – LED, 10mm white (or use your own)