If your garage door opener has the ability to use a wired switch, the most simple and cheap way to do this is with:
esp8266 http://r.ebay.com/SziJAO $4
5v relay http://r.ebay.com/kuAZTs $5
ST_Anything [RELEASE] ST_Anything v2.9 - Arduino/ESP8266/ESP32 to ST via ThingShield, Ethernet, or WiFi $FOSS
Optional
tilt sensor http://r.ebay.com/89YM7N $23
I have used these setups for all kinds of switching and monitoring, things like:
I retrofitted a chest freezer with a door sensor and a temp sensor, and SmartThings now can send an alert when the door is left open, or if the temperature rises.
I monitor the temperature of my water heater in the garage.
I built my own SmartThings setup for turning my sprinklers on and off.