Let's face it a new home and family, possibly an older pet are just to exciting and interesting to him learn about, so all his concentration is spoken for already! It's up to you to watch his behaviour and set times during his day to focus what little attention he has on the more basic aspects of fitting into family life. With consistency, patience, lots of praise plus a mop and some Stain and Odour Remover eventually your little puppy will grow into a young dog who has learnt some bladder control and where it is acceptable for him to relieve it.
Depending upon whether you are at work during part of the day or at home with your puppy will make a difference as to how long it will take for your puppy to become fully house trained. It depends primarily on you though, get it right and it shouldn't take more than a few weeks, although, like people, some puppies learn quicker than others.
Learn your puppy's signs and body language that he he needs to go to the toilet. First thing in the morning, after a nap,a vigorous play can all be triggers for most puppies, but generally regular toilet times are governed by how many feeds and at what time he eats. Depending on his digestive system will dictate when it comes out - watch and learn! Sniffing the floor, circling an area, are all signs that he is looking for a place to go. Take him to the area you want to use and stay until he goes - as soon as he begins to relief himself give a vocal cue such as 'wee-wee's' or 'toilet' so he begins to associate the word with the action.
If you are out for part of the day crate training is a great way to house train your puppy, as dogs are essentially very clean creatures and do not like to soil where they sleep so they will try to "hold it" until they can relieve themselves in a different place. The crate must be big enough so that your puppy can sleep, have food and water, turn and move freely but not large enough so he has a corner that he can use as a toilet and sleep far away in the opposite corner.
Puppies as young as 8-9 weeks can control their bladders and bowels for up to seven or eight hours, but if you are out for more than a few hours at any one time, it is unreasonable to expect a young puppy to hold himself for long. Select a larger cage and use Wee Wee Pads puppy training pads, either in the cage itself or (if you leave the cage open and he is confined to one room) outside the cage close to a door he will eventually walk through to go to his toilet area. Wee Wee Pads are treated with a chemical that encourages puppies to relieve themselves on the pad, helping to keep your floors protected and disposal of the waste easy and hygenic.
If you are lucky enough to be at home with your puppy, as soon as you see signs he needs to relieve himself pick him up and give a voice cue such as 'outside'. Take him to the garden or place you have designated and give another vocal cue for him to relief himself. Pick a phrase that WON'T come into everyday use such as 'wee-wee's' or 'go do it', just in case you end up with such a well trained dog that everytime you repeat the word you have chosen, he attempts to run outside and relieve himself!
As soon as your puppy relieves himself, give him lots of praise, so he knows what he has done is correct. Don't play with him, but take him back inside immediately so he learns the words you used means for him to go to the toilet. If you want to play, take him out again once you have taken him inside with a different vocal cue such as 'lets play', so he learns the meaning of the different words and associated actions he is expected to do.
Never, punish or scold your puppy for soiling in the house, even if you catch him in the act. Pick him up and without raising your voice, say 'No!' and take him the area he is supposed to use. When he finishes, praise him. Punishment will only teach him not to relieve himself whilst you are present. He will look to move away from you when he needs to go and if you are outside, that could me he goes indoors to empty himself - the exact opposite of what you are trying to achieve!