I was considering using a Raspberry Pi controlling a USB Relay to dim 12V LED lights, but I'm having trouble finding a solution that isn't a simple ON/OFF. What type of device would I need for dimming?
You probably want a PWM (pulse width modulation) solution. Essentially this means flashing the led on and off faster than you can see. To make it brighter, you increase the amount of on time versus off time.
You could use an external PWM LED driver, or possibly you can produce PWM from the GPIO ports on the Pi and step it up using a transistor and / or relay.