A Joule Thief (JT) is a step-up voltage transformer based on the working mode of a PWM (Pulse Width Modulation), it produce a oscillation in a inductor with the help of a transistor (2N3904, 2N2222, ...) then the output of the inductor is your new voltage. The result is that you can light a white, blue or even a ultraviolet LED with a single 1.5V cell (AA, AAA or any type of cell, i have used a watch cell too). This "voltage booster" circuit is not very efficient but it can use batterys that are near depleted. I whud not power up a microcontroler are anything that whud be disturbed by the voltage and power oscillation of the output, there are some dedicated step-up voltage boosters like the IC from Maxim with a 90% efficiency. With a bigger inductor and another transistor it is possible to get some very high voltage, i have see on the web some JT that can light up a neon tube from a 12v bike lead acid battery.
Step 1: Tools
Solder iron, Dremel, Hot Glue, Cutter or Exacto Knive and ... a pair of hands .