I love love love having a dog door. I've housebroken 4 Italian Greyhounds, and 3 GSDs with a dog door available.
I'll use my 1-year-old-tomorrow Russell as an example. I got him when he was somewhere between 9-10 weeks old. I literally took him outside every 30-45 minutes, and I think that was the key to making him understand that OUTDOORS was where you peed and pooped. He never got a chance to have an accident in the house because I swooped him outdoors so often. At the same time, I also taught him to go in and out of the dog door. Of course, he thought that was so much fun to have a portal to the outside world. I have a very secure dog yard, so safety isn't much of an issue. Being a smart boy, it didn't take him long to figure out he could go out and pee and poop without my assistance. I didn't rely on him doing this himself, but still kept taking him outside constantly.
As for not knowing what to do if there is no dog door, or if the dog door is closed, my dogs will jump on the door to let me know they need to go out. They know that doors lead to the outside. They do this when we go to a dog show, and stay in a hotel room. If one of them needs to go, they go to the door. If you don't want them jumping on the door, you could always hang bells and have them touch those instead.
~ Diane in Okla
Carly ~ AKC Champion, GCh pointed, HIC
Sage ~ AKC Ch.pointed (13 pts - chasing that last major), HIC
Russell ~ the big boy
Zelda ~ 14 yo puppymill rescue Italian Greyhound