For house breaking puppies we don't take them out on a timed schedule; we take them out based upon behaviors. If we cannot watch them very closely we have them confined in a small portion of their crate (dogs, even puppies typically don't want to lay in their own mess). If we hear them stir after a nap in their crate we take them out. If we hear them whine while in their crate, we take them out (it's not uncommon for them to learn whining will lead to them getting attention and then we'll have to modify how we respond to their whining). When we get them out of their crate we first take them out. While they are loose in the room with us we watch them very closely; most puppies (and dogs) have behaviors they do when they need to go to the bathroom (these behaviors can be individual and different for pee and poop) and when they display these behaviors we immediately take them out. If they have been running around loose in the house for a while, we take them out. Overnight, we keep them in their crate and restrict access to water. When we hear them whine during the night, we get up and take them out. When we take them out they are on a lead and we say "hurry-up" when they relieve themselves and then praise them. They don't get to play outside (be off lead) until after they go to the bathroom. We will use this command when we are traveling with our dogs; bathroom breaks with 6-9 dogs walked on lead are easier when they will go on command.
Following this method we have found most of our pups will learn to go to the door we take them out through when they need to go to the bathroom.