I'm Dr. Jo and I'm here to help you with your question about your puppy. I'm so sorry you're having this difficult and frustrating problem, but glad you're looking for the information you need.
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Even though this can be an extremely frustrating situation, I've got good news for you. There are a multitude of resources available that you can read to learn how to successfully house train your puppy.
There are also a lot of different methods, so you can choose one that seems most suited to you in your unique situation.
After counseling many puppy owners over the more than twenty years I've been a veterinarian, I am convinced the best method is "crate training
." This method capitalizes on a puppy's natural instinct to avoid soiling his bed. I'll attach more detailed information below, but the basic premise is this:
1. Get a crate (dog kennel carrier) that is only large enough for your puppy to stand up, turn around, and lie down in.
2. Keep your puppy in this crate AT ALL TIMES when you are not actively engaged in playing directly with the puppy to such an extent that going to the bathroom in the house simply isn't an option because you're watching him too closely.
3. Every time you take him out of the crate or put him back, take him outside and give the option to go. Praise him if he does.
4. Repeat. Repeat. Repeat.
5. If you are busy playing with him in the house and he starts to look like he wants to find a place to go to the bathroom, tell him NO!, pick him up and carry him outside and give him a chance to go outside. Praise him if he does.
Please note this is not to say your puppy has to spend a lot of time in the crate, and it is not cruel. Take him out of the crate as much as you can, but YOU MUST WATCH HIM closely enough to prevent accidents before they happen, or at least interrupt him as described in Step 5 above.
Please also understand the crate is a happy place and crate training is not cruel. That being said, there are still no short cuts and no excuses.
And, as a final note, please understand that in your situation you can expect this to be more difficult that it would be if he had been successfully crate trained earlier. I say this because a 4-month-old who is going to the bathroom in the house has essentially been trained (however inadvertently) to actually GO to the bathroom in the house by way of poor technique by an inexperienced owner. It takes longer to undo the training the puppy gave itself.
I'll attach more information below, but that's the best plan.