I just realized that I could need a small flashlight for my keychain. Fritzed together, here it is :P Main goal was to keep it as minimalistic as possible. Powered by a small battery cell.
It's a really simple project. You'll just need a LED (which should be bright ;) ), a resistor for the LED, a button, and a battery. In most cases, you should add a voltage regulator, too.
Simply, Battery GND (-) connects to LED GND and Regulator GND; Battery + goes into the Regulator In, the resistor connects to Regulator out and to the button. The button connects to LED +.
Connect everything. Insert a battery. Press the button. ;)