How would I add a relay to turn on a new device when the car is on?

Dont throw a relay in there, theres no point.

Like stated above, use the ignition wire or accessory wire at the steering column, going to the key cylinder.

Black/Red = Ignition wire
Blue = Accessory wire

Both will switch when the key is on and off. Make sure you use a inline fuse. 10 amp would be more than enough.