We just this spring condo-trained a rescued pit bull puppy who started out pretty much as a blank slate – she was found on the street and had few clues as to how to interact with people or dogs.
My technique was based on three primary pillars:
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All positive. I wanted to stay away from punishment, from nose-rubbing, from “smacking”, and even from “NO!” itself.
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Crate training.
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Frequent opportunities to go.
These three are all related in a way. The crate isn’t punitive – it serves like a natural den. The puppy is naturally reluctant to soil her (ours is a girl, so I’ll use that pronoun) den/sleeping place. As noted above, see numerous sites on crate training. The frequent opportunities not only are necessary because of the tiny puppy bladder, they are frequent chances for the puppy to be good and get reinforcement as a good dog. Also, frequent trips save your household and your nerves.
I know it’ll be a pain in the keister – but reflect that most things done well are done well by dint of effort. We got up all the time, comfortable or not, after supper, before bed, whenever we came home, whenever we noticed “it had been a while.” Certainly at least every 2 hours except for overnight slumber, which should probably be in the crate at first. Up and out, up and out, that’s your motto.
Whenever the puppy did go in the house, here’s what I did. JUMP up, get a paper towel wet in the spot, and rush outside with the puppy (leashed). Set the wet, smelly, urine-soaked paper towel in the grass where I wanted her to pee.
Then PRAISE HER.
No punishment, no hitting, no humiliation. She probably doesn’t remember consciously deciding to be bad – she just had to go, it’s natural. But she very quickly picked up on the “hey, I get praised for this, if I go out here!” aspect.
You want her to think inside=my den=no soiling, versus outside grass=relief=praise.
That’s really all I did. I also think leashing up at the threshold helped establish more clearly that “this is our den, no peeing.”
We brought her into the house April 2. She knew what do do by Easter, which was April 8. She did have accidents after that of course, mostly when we got lax about taking her out aggressively. She had some illness including diarrhea in late April that caused a few house (and one crate) accidents, but she was a sick little girl, I don’t blame her. She hasn’t had an accident in the house since May, and that was under family stress (the humans were moody) and I don’t blame her for that either…and she only had a few little accidents over the whole stressful month of May.
We let her sleep out of the crate overnight (in a doggie bed in our bedroom)…um…I forget when exactly, but she transitioned pretty easily to the doggie bed at night (it may have helped that we have an older dog snuggled happily in the doggie bed right next to hers).
It wasn’t long before she was waking me up with a whine or by placing her paws on the edge of our bed, even when she had diarrhea. I can’t tell you how proud it made me that she’d wake me up and hold it until we got outside even when she was pretty sick.
So, my experience may be an anomaly – this is the first time I’ve ever been fully in charge of housetraining a puppy. But despite many strikes against her, our puppy did a great job, and we kept everything positive.
Think of it this way: you’re building a relationship with an innocent, not merely guarding a carpet against a vandal.
Best of luck to you! Now, where are the pictures??? 
Sailboat