You first have to set the current to match the LED that you have. That board has 3 choices 0,35A – 0,7A – 1A.
Connect it up to a power supply of voltage 6-30V. With the higher voltage you can connect several LEDs in series to be controlled at the same time.
Connect the ground of your power supply to the ground of your Atduino.
Connect one of the PWM pins to one of the board's input.
I have a feeling I need to create a complicated sketch to interface with the shield
No, just use the analog write function.