When someone adds you as a friend, you need to confirm that you want to be friends with them. When you have a friend request, your Friends Tree will shake its branches and an exclamation mark will appear on the tag in the pot holding your tree.
To see your friend requests, click the tree. The requests will be highlighted in orange and you can then choose to add them or to block them from contacting you again.
For safety,you should only add friends you know, and ALWAYS ask your parents before adding friends to your tree.