A Friend is added when you send a Friend request and it is approved by the receiver, or when you approve a Friend request sent by another user. There are two ways to send a Friend request: by tapping on an avatar that is within a certain proximity of you, or by searching for a user from the user search screen and sending a request. When you receive a Friend request, you will be notified via a pop-up window.
You can view and respond to Friend requests from Main Menu > Friend/Party > Friend Request.