The circuit is as simple as it gets so you probably already have most of them.
You will need:
- arduino board
- bluetooth serial module (I used a btm222 module on a breakout board with an inbuilt regulator )
- an LED
- resistor (100ohm)
The only problematic part here is the bluetooth module. There are different modules all over the internet so be sure you check the pinout in the datasheet of the one you get as it can differ.