Sharing and Taking Turns
At one year of age, children have not yet developed the social or emotional maturity to play together, whether in pairs or in bigger groups. For one-year-olds, the term “playing together” means little more than sitting near each other. Each child is absorbed in her own individual activity. The children do not share games, toys, or imaginary play; the most they can be expected to do is perhaps take notice of each other's toys and maybe try to take what they find interesting for themselves. While they enjoy being in groups for physical fun like singing or dancing, they don't actually share the experience with their friends by singing or dancing with each other. Instead, one-year-olds view the experience as their own — other children are just extensions of the moment.
If you want to get your child used to sharing, you're going to have to direct the play. Say that you have a ball that your child and her friend both want to play with. You might try sitting on the floor with them and rolling the ball first to one and then to the other. Again, the children will be playing near each other and with the same toy, but they are not really playing together. Do not expect them to take turns. That's a lot for them to grasp at this age.
When playing in groups or with another child, your child will enjoy rolling balls, playing with large puzzles, dancing, singing songs (especially ones with clapping and hand movements), finger painting, and playing outside. Most children also love dress-up at this age, not so much for the possibility of pretend play as for the challenge of getting in and out of the clothes and seeing how different they look in the mirror. In fact, it's a great idea to have a large mirror around, as young children love to look at themselves. When it comes to toys, it's best if each child has his own to avoid the disputes that are so common at this age.
It's largely a waste of time to ask a child “Why did you do that?” Simply set an example. “John didn't know you were still playing with that block, James. You can have it back.” Then give John another toy. Fairness is important, as chances are James will take a toy from John in a moment.
Because it is unrealistic to expect a one-year-old to share with others or to engage in self-directed play, you will have to encourage and take part in playing with your child and her friends. They will want you to play with them, anyway, and will bring blocks and other toys over to you (even if you're busy). It's helpful, then, to realize that your presence is necessary. They are watching you closely to see how you play, share, take turns, and enjoy yourself.
Your job, if you are playing with your child and any of her friends, is to offer them all the same instruction, praise, guidance, and correction. Do not be tougher on your child because you want her to make you proud and do not, on the flip side, play favorites with your child. While this is often difficult for a parent, your child wants to see and hear fairness more than she wants favoritism. This is what she will encounter out in the world, and by setting the example of kindness and fairness you will help her be a good friend when she is ready to be one.