Well you said you have found tutorials on how to set up a WiFi webserver on your arduino, a quick google search yielded this as one of the many results: http://marioboehmer.blogspot.com/2011/01/wifi-webserver-with-arduino.html
. I am sure there are many more out there.
Once you have set up a webserver to your liking, which can be accessed from within your local network, you have to set up port forwarding on your wifi router, that sends any port 80 requests to the IP address of your arduino. Then, if you, like most, have a dynamic WAN ip, it would be very useful to set up dynamic DNS forwarding, so you pick a free domain name, say test.dyndns.com (there are other services as well) and this redirects to your home IP address, and thus, where requests are forwarded by your router to your arduino. Ta-da!
Keep in mind you will need parts to interface with the garage door as well.