How can I get my puppy to calm down?

Exercise is probably the best bet. Think about a puppy. They play hard for an hour or two just like a child. You look at them and you think, ""Oh my God, where did all this energy come from?"" But then right after that it's lights out and they're going to be asleep for an hour or two.
So with that being said, the best bet with a puppy? Play with him. Give him an outlet for that energy. Take him for long walks. Play fetch if they're old enough to do that yet. Anything that's going to use energy, use their mind, that's that's what they're bred to do. You know, they're pack animals. They’re normally roaming around with other dogs all day long or sleeping. That's not going to change just because you got them and brought them into your home. So they still need those basic essentials. 
Let them be a dog. Let them explore. Take them for walks, do those things to burn off some of that energy. And I will tell you one other thing, too, as far as training goes, the best time to train them is right after you've done that so their energy level is not so high. They’re in a better mental state where they're more relaxed and much more amenable to learning new things.

Time and exercise, as puppies will just go and go and go. They're Energizer bunnies until they're not. And then they collapse and fall asleep for a couple of hours, but you want to work with them and get their mind going. It's more than just trying to have them exercise and run and play. You also want to be working with training. Puppies can start learning as early as just a few weeks old. And so, by training them, you're not only working their body, but you're also working their mind. And that can help calm them down and hopefully help your relationship and make you a lot closer.