Step 1: Electrical Schema
The bicycle dynamo works as a current source - it always "tries" to deliver its typical 500mA of current. This is an ideal source for light emitting diodes, which are current driven. The 500mA is way too much for single diodes, but it is just good for modern power LED (such as Luxeon, SSC, Cree etc). Power LEDs are delicate when it comes to reverse voltages, so we will rectify the dynamo current to power them.
The circuit is super simple - the graetz bridge rectifer, some smoothing capacitors and power LED diode.
Red LED diodes for the tail light are put as one branch of the rectifier. 13 diodes are connected in parallel - that multiplication gives more light and splits the current on more diodes (as You know, one diode can take only 20 ~ 25 mA current).
Please note, that the bicycle frame is usually used as the ground in AC dynamo circuit. The rectifier on the AC side is connected with the dynamo and with bike frame. The DC circuit needs 2 wire cable for its connections - there mustn't be any electrical contact with the frame.