Supervise toddlers at all times.
Playing with others is essential for toddlers because it helps them learn share, communicate and build friendships. Getting multiple toddlers together can also be a headache, so it's best that play dates last no more than two hours and no more than two or three children play together at the same time. The gender of your toddler's playmate doesn't much matter, so invite any well-behaved toddler over.
Art
Most toddlers love getting messy. Creating art projects together also allows a shy toddler to get comfortable with her new playmate, since she can work independently while also being next to another toddler. If you can handle the cleanup, finger painting is an activity most toddlers will love. Spread out paper outdoors on nice days and ask the playmate's parents for permission first, since she'll likely end up covered in paint. Water-color painting or gluing feathers and yarn to paper also gives toddlers some fine motor coordination practice without being quite as messy.
Outdoor
Outdoor play gives toddlers a chance to run around and work off some energy while also getting exercise. An activity as simple as a walk around the block or a trip to a local park can keep toddlers entertained for an hour or more. If the weather is warm, pull out a sprinkler and let the little ones run through it. In cold weather, bundle them up and make snow angels or go hunting for animal tracks in the snow or mud.
Games
Games aren't always easy for toddlers, but playing them with others gives toddlers a lesson about sharing and cooperation. Of course children this age won't be able to follow directions on most board games, but simple games that require turn-taking will be possible. Set up a bucket and find a soft foam ball and ask toddlers to take turn trying to throw the ball into the bucket, or set up a simple obstacle course that requires toddlers to crawl around and jump over obstacles such as pillows.
Free Play
Some toddlers will sit and focus on a puzzle for an hour, while others can't seem to sit still. Setting out a variety of activities may result in a very messy playroom, but it gives toddlers a chance to try out a number of activities together. Set out blocks, puzzles, toy trains and cars and dress-up clothing in different areas of the room. Toddlers may each gravitate toward a different activity, so sit down with them to facilitate playing together. Call both children over to a puzzle or pile of blocks and encourage them to work together to do the project.