I want to build a small generator
Ok, just wrap a bunch of coils of wire loosely around a stationary magnet , and move the magnet back and forth. With enough coils, you can light up an LED. Attach a honkin' capacitor to it, and you have a home-made 'shake' flashlight.
if you just want a little one for like 2 or 3 plugs to charge your phone and lil things you can buy one of those battery back up things at staples