The general concept: TV remote sends IR signal to IR receiver, IR receiver sends data to Arduino, Arduino triggers a relay which is connected to the M232 power button, power button turns the lights on.
I used a solderless breadboard for initial circuit design. When I was satisfied it worked, I soldered all components onto a breadboard.
Monkey Light M232 - http://www.monkeylectric.com/m232_bike_light/
any remote control - I used an Apple remote 'cuz it's small
9V battery w/ connector lead
7805 voltage regulator https://www.sparkfun.com/datasheets/Components/LM7805.pdf
Arduino - I used a Pro Mini https://solarbotics.com/product/50725/
IR receiver - I used a TSOP 4038 https://solarbotics.com/product/TSOP4038/
5V relay - I used an Omron M5SB-14 http://www.omron.com/ecb/products/pdf/en-g5sb.pdf