House training is the same method whether training a puppy or an adult shelter dog. The main goal is to of course to go potty in an appropriate area & time, but the communication learning is for both dog & humans. The people in the dog's life have to pick up on the DOG'S cues that it has to "go". Some examples: Does it pace, whine, sit by the door, ect.
Schedules matter. Most dogs want to go potty within 15 minutes of eating. Times of excitement like when the family comes home from work and school or getting up in the morning are times when the dog should go out immediately to prevent accidents. Having a set schedule will teach your dog to "hold it" knowing that it will go out before the dog becomes so desperate that it has an accident.
Take your dog out frequently at first, use a command like "go potty" and don't play with the dog until after it has gone potty. Praise immediately & happily for a job well done. If the dog doesn't get praise or a treat until it comes into the house, it will associate the reward with coming in, not for going potty. Never punish the dog for having an accident. The dog will only associate you with inconsistent behavior & submissive stress piddling can develop.
Crate training is used to keep the dog in a confined area so it doesn't want to soil itself. The method works best for young pups but dogs form puppy mills usually were forced to live in filthy conditions so they don't know not to "go" in a kennel. Some dogs can't handle the confinement and will "crate fight" to get out and can be a danger to themselves, so anytime a crate is used, be sure to stay close and observe your dog at first to see if it is a safe method of potty training for your dog.
It is best to walk your dog on a leash at first so it learns not to play but what it is being asked to do. Play time comes after. Constant supervision in the house is key also. The dog can run into another room and back before you realize it left the room. Using a leash tied to your waist or chair will keep the dog with you or use a baby gate to keep it in the same room.
Remember be patient & consistent in training. Keep the dog with you and observe it for the signs telling you it needs to go outside. Accidents will happen so clean it up immediately with a product such as Natures Miracle or Skout's Honor made specifically to clean up pet accidents.