How quick the dog gets potty trained depends on how consistent the training is. If you give the dog lots of praise and reinforcement and plenty of opportunity to have success, it learns pretty quick. If mixed signals are sent then it could take much longer. A pup can not be expected to have bladder control until around 12 weeks. Up to that point when they have to go, they have to go!

If you are crate training properly the pup should be trained by 12 weeks old.