Be persistent! Make sure the puppy doesn't get the opportunity to pee and poop by using a leash indoors or confining him to a crate when you're out. Depending on the puppies age, pop him outside every 20 - 30 minutes, so there's a greater chance of him toileting outside (by accident at first.) In addition, get rid of any scent markers he's left by peeing or pooping indoors, as these will draw him back to the same spot. This means cleaning the area daily, for 2- 3 weeks after he last pooped there to fully get rid of any lingering odor that the dog can detect.
Many owners appear disappointed that their young puppy will not toilet when out on a walk, yet relieves itself the second it gets back home. This is because the puppy has been taught to toilet only at home (hopefully in its garden), and being creatures of habit, they often wait until they have returned home before evacuating their bladder and/ or bowels.