I'm racking my brain trying to remember everything we learned during puppy training class. LOL. We bought our Westie at around 8 wks and had the pleasure of house training her. Boy...what an experience! I don't remember how long it took, but I do remember at the time it felt like an eternity.
I remember our trainer telling us to reward her good behavior (going outside) right then and there...like outside, in the middle of the yard. (Keep a couple treats in your pocket every time you take her out.) You need to condition her brain to realize that the good behavior is peeing/pooping outside, not coming back in the house (when she is probably getting her treat). It's basically just repetition. She will learn eventually.
Another thing is were told that a dog will not soil their living space (assuming they are confined to a crate). We used this method with our puppy. I suppose in theory thats correct, but I can tell you, that on several occassions, we came home to her sitting in pee/poo in her crate. I think more importantly is to remember the rule that our trainer taught us. A puppy can only hold it's waste for 1 hr + # months old. So a 1 month old puppy can hold it for 2 hrs, and after that you are asking too much. Granted that simple equation doesn't work forever, but for the very new puppy, I think it helps. So when training, keep that in mind and take puppy out before that time frame expires.
I hope this helps, I wish I could remember more! Good luck to you. Just know that it takes patience and persistance.