Where can I find an electric generator that produces electricity when spun?
Since you are new to electrical circuits, I would suggest using small DC motor as generator to get the "feel" of how circuits work before buying an actual generator and getting into serious stuff.

A DC motor can generate electricity when it's shaft is spun(although it is not designed to do this efficiently, it will work just fine for simple applications). Get a 3v or 6v DC motor from an electronics hobby shop. Fix it to the frame of the bike such that the shaft of the motor touches the metal rim of the tire(You will have to find a suitable rubber bearing to make firm contact). Connect a 3v LED and a 470 ohm resistor in series across the motor terminals. Spin the wheel of the bike. The LED should light up. Enjoy!