When puppies cry at night they will usually continue to cry at night for around 2 to 4 weeks and as the puppy gets older the less they will cry.
Just like a human baby will cry for around 6 months of it's life a puppy will cry at night until it matures but that usually doesn't last as long as crying in a human baby.
So about all you can do is wait it out until the puppy gets older and within a couple weeks to a month or two the puppy should stop crying at night.
Sometimes you can keep the puppy from crying at night by putting a plush dog with the puppy and they will not feel alone then.
Or if the puppy is near it's mother or siblings then they tend to cry less at night.