If you are considering crate training, please see “Is crate training a good idea?”
Let me offer an alternative method. I have been through many methods over the years, dozens of times. Here is the best one I’ve found.
Keep to the same strict diet that your pup was on when you picked him up. Food changes, even a morsel of a doggie treat, will cause diarrhea. Use the same food your pup was on. Do not switch foods during training. Do not give any other food or treat at all.
First, remember the primary goal is to establish a communication between yourself and your new pup. You need to speak the same language. The more you can see each other, the better, as you will start off with visual cues. Place your pup in an area where you can observe him. I like to baby gate off a room with a hard floor, such as the kitchen. When he begins to act strangely, (quick movements, excessive sniffing in different locations, etc) I know he is ready to explode. Grab him, and get him outside. Leave him at least five minutes. If it was a false alarm, no big deal. Bring him back inside, and keep watching him out of the corner of your eye. (Remember watching the children?) Repeat this process as necessary.
Let’s say that you missed his cues. (You may swear he didn’t even give one, but he really did). He went to the bathroom on the floor. Its O.K. Chances are he went to the far end of the room to go, and he won’t be wearing it. The idea is to let him put distance between himself and the lovely gift he left for you. Otherwise, he gets used to having it in his environment, and then you have a challenge! Since you have a hard surfaced floor, a few paper towels and some disinfectant will take care of the problem. (Don’t worry – it’s only temporary). Don’t bother fussing at him at this point. He won’t understand.
If you see him in the act of going, make a loud guttural noise that will scare the hair off him. (Pretend you just found your little brother spray-painting your first car). This will make his muscles tighten, and he will stop for a few seconds. Get him outside, and leave him until he goes, even if it’s fifteen minutes. (Unless he finished in the house). Remember, puppies get bacterial infections just like babies, and there may be a time when he has to go several times in a row, or even has diarrhea. He will have very little control, and very little warning. Just ride through these times. Your pup will be housebroken within a week, which is a lot better than a baby! Remember not to hold it against him if there was no one to let him out when you were gone, and he had an accident. If you come inside after an unsuccessful attempt and then he decides to unload, that means you did not stay out long enough.
For the occasional puppy that just doesn’t get it by his tenth week, you may need to use some negative reinforcement. (For those really frustrated few, please put the baseball bat down). Just a simple fussing will do. Let him know you are displeased, but don’t rub his nose in it. Just take him to the vicinity. He will know it’s there better than you. You know you have succeeded in getting through when he quits smiling, and his tail quits wagging. This aggressive approach should be reserved for puppies with normal bowel movements, and no diarrhea.