Here are some of the devices and products shown in the video. There's no connection between the vendors and me, it's just where I found (or bought) the stuff from originally. I'm sure there are others who sell the same.
- Avago Blue LED
- TI TLC5940 PWM Constant Current Driver
- Rigol Multimeter
Here's some resources to learn more about resistors, LEDs, Ohm's Law, and an easy tool for calculating current limiting resistors.