You normally drive a relay with a microcontroller using a transistor: just a simple BJT, a darlington pair or a power mosfet (it depends how much current your relay draws). Here's an example circuit: http://www.uoguelph.ca/~antoon/circ/relay5.html. Don't forget to put in the back EMF diode across the relay coil, otherwise you'll eventually burn out the transistor.
Looking at your problem though, if i was you i'd have power going to the micro all the time and have the micro sit in sleep mode with an interrupt pin connected (indirectly via a transistor) to your accessory line. When your accessory line changes, power your motor and open / close the automatic screen.