First of all, I would leave the puppy with it's mother for 14 weeks, though some breeders keep them longer. This will aid in a more confident puppy and housebreaking will be easier.
Feed a high quality food. Low quality (cheap) is full of filler and the dog needs to eat more. This means more coming out the other end.
Keep the puppy near you and in a confined area, like just one room so that you area aware of "I gotta go!" and are able to get him outside soon enough. Keep a treat with you and the second he starts to go, get the treat out and have it at his nose the instant he is done peeing or pooping.
When going out, always have the puppy sit at the door, but not so the door will hit him when you open it. When you open the door, say "out" and praise when he walks through the doorway. This teaches door manners and will let you know when he needs to go out.
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I agree with the Ian Dunbar recommendation. While it's pretty normal for toy puppies to stay with the breeder for 12 weeks, due to the high chance of them crashing from hypoglycemia, a lot of standard poodle breeders send the puppies off to their new homes by 9 weeks.
See if you can find puppy kindergarten classes to help with socialization. There's a bit of disagreement over when to start classes. Some folks say to wait until after vaccines are finished, which is usually around 12 weeks. Others, including one of the rescues near me, wants puppies to start in class ASAP to reduce the chances of badly socialized dogs later ending up in rescue or being euthanized for behavioral issues. There's really no perfect answer.