how do i store the energy produced when cycling so that it can power the bike's lights at night?

Answer 1

Here you go, Peter Jon White knows just about everything about dynamo bicycle lights:

http://www.peterwhitecycles.com/lightingsystems.htm

Answer 2

you need a generator or alternator and a battery.
also, a light sensor or timing circuit is useful

when the light intensity drops below a certain point, it closes the circuit to activate the lights

alternatively, you can have the lights come on a timer

of course there should also be another on/off switch to turn on when you want to ride it, because you wont want your bike lights to go on when your bike is just sitting in the garage.

Answer 3

connect a dynamo from the wheels to the battery
the rotation of the wheels will charge the battery
connect the output of the battery to bike lights