I would like to turn the backlight of an LCD Display on and off (ideally the arduino itself should be able to do this, and not some button or so). It's not supposed to fade, a simple on and off would be enough. How can I do this?
Also: Do I actually need a potentiometer? Or could I do it in some other way? (As I don't wan't to adjust the contrast or so while the arduino is running)
You can just use a transistor like 2N2222 or a logic-level MOSFET. Instead of connecting the cathode of the backlight to ground connect it to the collector of the 2N2222, then emitter to ground. Connect an Arduino digital output to the base through a 220-ohm resistor (not a critical value).
The Flexible MIDI Shield: MIDI IN/OUT, stacking headers, your choice of I/O pins
This project does just that with the LCD back light:-