I'm trying to build a controller that can take a 0-5V signal and use it to control a 12V motor.

Ideally, I'd like there to be a gain curve where
0V=0V
>~3V=12

but the easiest way to do this would be a simple on off switch controlled by the Input voltage.

with my limited electrical knowledge, I think I am looking for a transistor.

if I wired a variable resistor to the transistor, I should be able to adjust the threshold at which the 12V circuit is opened...right?