The most important life skill your child will ever have is - making friends.
As a parent, it is our job to prepare our children for the grown up world, and everybody knows the only way to succeed in life is to get along with others. We start when they are born, their first introduction is to their parents, their siblings (if they have any), and then their grandparents and extended family. They develop their safe zone of people, arms they feel secure in, and faces, smells, sounds that comfort them.
When babies grow, can walk on their own, their curiosity propels them into the paths of others. We use the term "making strange" when our child tears up and cries in the presenses of someone new. It is here, in these moments, that we begin to introduce our children to making new friends, and teaching the difference of friends and strangers.
Everyone is a stranger until they become a friend. Upon meeting another child, or being left with an adult caregiver, your child will look back at you for guidance. Smile, encourage, get down on their level and look at the new person as they would. They might need a hug for reassurance, or just a few kind words. What ever it may be, make sure you child knows you are behind them where they can reach you while making this introduction.
Introducing toddlers to other children their age can be as easy as making a play date. It might not be a good idea to walk up to any parent and child combo on the street to inquire about playing together, but you can certainly show your child how to be friendly by saying, "hello" as you pass them by, or smile and wave.
When at the park, give your child a little space. Don't force your toddler to play with a bunch of kids if they don't want to. Let your child establish where in the park they want to play safely by pointing out suggestions. If their are other toddlers around, keep close to their parents and join in conversation. By you making first contact with other parents around, you are demonstrating to your child how to make new friends. Most of the time you will find your child imitating what they see you doing.
Join a playgroup that meets on a regular basis. I highly recommend MOPS (Mothers of Preschoolers) where mothers and their young children can develop new friendships. Check community calenders and check local preschools for opportunities for your child to socialize with others their age. If your child doesn't participate the first few times, that is okay, they may need a time or two to adjust and join in. Look for things that interest your child, like books, puzzles, or drawing and encourage your child to join in these activities along side other toddlers.
First encounters between toddlers will not always be pleasant. The first meeting between two children could be over the dispute a sharing issue where toys are involved. Toddlers will not always get along every moment of the day, but occasionally bond through their diversity. When your child is in a dispute over sharing gently step in and give them guidance by promoting turn taking, and giving the other child the toy even if your child had it first. Your child might not understand this at first, but later in life they will thank you.
Don't force your child to make friends with another child just because you are friends with the child's parent. Toddlers have a mind of their own. You should respect, after all attempts have failed, that your child may not want to be friends with another. Talk to your child about it, why they don't get along, things they can do to be nice, and make sure to express how much you appreciate them making an effort to get along with the other child. Your acceptance and approval is very important to a child at this stage in life.
Above all, don't fret. Even the shiest toddler will step forward at some point and make an effort at friendship with another child. You need to give them time, encouragement, and support. Soon your child will be off playing with more friends then you, yourself, can count. All thanks to the role modeling and life skills you are imprinting on them.