@acmefixer
That looks pretty good, cheap and simple. Should be small enough, too. What kind of battery life could I expect from this? Would I need to put a higher value resistor in for only 1 LED? Could I put a pot in line, adjust to get the brightness I want, then check the pot for the resistance value, then know what reistor I want? Like I said, I am a beginner with electronics. I undertsand volts, amps, reistance, but not familiar with coils, inductors, tranistors. Would appreciate explainations if not too much trouble, and description of how that Joule Thief thing works. Also, MOSFET KILLER said something about putting 2 batteries in parallel to get more current. Is this an option with this type of circuit? What if I wanted to add an LDR to automatically turn the light on at night? I considered the solar cell to recharge the batteries, but don't know if they make a solar cell small enough to fit my clocks, or have the power to give a good recharge. Also, would not know how to wire that either.
I really need to keep these simple and cheap, because if they work OK, I would like to start selling the clocks with the lights in them. They look cool, but can't make them profitable with expensive parts, and won't have happy customers who constantly have to change batteries or are unsatisfied with the quality/performance of the lights.
Thanks for the help so far, everyone.