Puppies frequently experience short periods of hiccups, mainly because they swallow air too quickly and their pulmonary muscles are not yet developed enough to recover. A hiccup is actually a spasm of the diaphragm and a momentary closing of the glottis, causing a contraction of the muscles. Hiccups in puppies tend to occur just after eating, and subside within a few minutes. Some breeds, particularly brachycephalic dogs, gulp air as adults and tend to have hiccups more often than dogs with normal sized snouts.
Slow down the rate your puppy eats, by either serving him small quantities at a time or using a dish that slows down fast eaters. Puppies who are raised with other animals tend to eat quickly, in order to make sure they get enough food. This is purely an instinctual response because in the wild a dog has to eat as much as possible as fast as possible. Since this mechanism isn't necessary in your home, you will need to work with your puppy to teach him to slow down.
Help your puppy to relax if he is in the midst of hiccups. Talk calmly to him and gently pet him. Never scare a hiccuping puppy, it can create fear aggression in him and can also cause him to choke if he still has food in his mouth. Scaring your puppy will also teach him to avoid you when he's hiccuping.
Be aware of any changes in your puppy's hiccuping, which could indicate a problem with the development of the pulmonary system. Gulping, wheezing and vomiting are all signs that need professional attention from your vet. If your puppy is regurgitating food as soon as he swallows it, suspect a blockage or hernia that will require surgical intervention.