Interesting idea. If I understand it correctly, the Pi is directly wired into the network and then its controls a relay to trigger the garage door. So figure 45 for the Pi (with shipping), $5 for the ethernet cable, and $5 for a good relay. Humm…about the same cost as getting a remote garage door opener. BUT this one you can control from the internet :).
http://www.raspberrypi.org/phpBB3/viewtopic.php?f=63&t=25118