“Down” can be taught very similarly to “sit.” You can wait for your dog to lie down (beginning in a boring, small room such as a bathroom can help) and capture the behavior by reinforcing your dog with a treat when he lies down, giving him his release cue to stand back up (and encouragement with a lure if needed) and then waiting for him to lie down again. When he is quickly lying down after standing up, you can begin saying “down” right before he does so.
Teach him to come when called. Come Jasper! Good boy! Teaching him to come is the command to be mastered first and foremost. And since he'll be coming to you, your alpha status will be reinforced. Get on his level and tell him to come using his name. When he does, make a big deal using positive reinforcement. Then try it when he's busy with something interesting. You'll really see the benefits of perfecting this command early as he gets older.
Never leave a puppy in his crate all day; he needs several bathroom breaks, as well as play and feeding times. Even though he won’t want to soil his sleeping area, if he is in there for extremely long stretches, he just might. (He can’t help it!) And if he does, it is because his owner has neglected his responsibility, not because the dog has misbehaved.
Imagine your puppy running out the front door. You call him, waving a treat. But he'd rather chase a squirrel into the road than come back to munch on a treat. In addition to the obvious danger of Puppy getting hit by a car, he learns that he doesn't have to listen to you. He learns that he's in charge of what he decides to do and what he decides not to do.