Puppyhood is the best time for your dog to make friends, because the older he gets, the trickier it can be. The way that your puppy makes friends is a little different from the way humans make friends, so when you're introducing him to other creatures big and small, take things slowly. He learns better if you take it one step at a time -- do that, and he'll love making new friends.
The first few months of a puppy's life are the most important for making friends and meeting other people and animals. Once he's 3 weeks old, he's ready to make friends, and he only has until he's about 12 to 16 weeks old. If he hasn't made friends and socialized by that time, he's going to have significant difficulty doing so later in life. While humans are generally able to make friends and meet strangers their entire lives, if your puppy doesn't learn how to do it within those first 12 weeks or so, he'll grow up fearing the unfamiliar.
When a puppy meets a human, he doesn't react the same way people do. He may show more hesitation at first, especially because humans come in so many sizes, shapes and styles -- he may be less frightened of a young girl than of a 300-pound man. One of the best ways for a puppy to make a human friend is for that human to offer him a small treat. Approach the puppy with the treat and allow him to come to you, and he'll learn not to fear strangers. The American Kennel Club recommends that a puppy meet 100 different people by the age of 12 weeks, so he is used to encountering a wide variety of strangers.
Meeting Other Animals
Puppies have to make lots of animal friends during their peak period of socialization -- otherwise, they can grow up fearing other animals. Your puppy definitely doesn't make friends with other animals the way that people do -- there's a lot more sniffing involved. After they get to know each other by thoroughly sniffing, they typically engage in a little rough-and-tumble play. Don't worry if they tackle or nip at each other, as this is just how puppies play. By meeting other animals at this age, he learns not to fear them.
Think of a puppy as a shy human -- he easily makes friends one at a time, but in an overstimulating environment, he can become overwhelmed and upset. Introduce your puppy to new friends one-by-one instead of at a party or a dog park, where the large grouping of strangers can easily intimidate him. If you don't want to meet new friends one-by-one, a puppy socialization or puppy kindergarten class -- organized and monitored by a licensed trainer -- is the perfect opportunity for supervised socialization.
A puppy remembers his friends -- and his foes. One of the reasons that puppies and dogs sniff each other as a greeting is because they use scent to learn about each other. Every animal has a distinctive odor by which he is recognized -- this is also why dogs love to sniff where other dogs have gone to the bathroom. If your dog doesn't immediately recognize a friend by his looks, his smell could be more revealing. Dogs are able to remember by looks, but sometimes in a more generalized way. For example, if your puppy is attacked by a dog of a certain breed, he may have an averse reaction to all dogs of that breed. This may even be the case with his own breed -- bad experiences with his litter as a puppy may make him fear his own kind.