With adult dogs and older puppies who are not housebroken, you often have more of an uphill battle because they have some undesirable habits to unlearn. There's a section on potty training dogs when they are older further down this page.
The key to success is the timing of IN and OUT. Young puppies take IN food or water and usually within 15 or 20 minutes, they pee or poop OUT.
So your job is to get the puppy to where you want him to be in time for that OUT moment.
You have a life and you won't always be there, even if you are just answering the phone. So cleanup is part of the process of potty training dogs.