To add someone as a Friend select the 'Add Friend' button on their profile.
This will send them a notification that you have requested to be their friend.
If they accept you will receive a confirmation notification.

Once you are friends you will be able to see their profile on your Friends list and be able to message whenever you like. If they have sent you a friend request, you can respond in your notifications tab (the bell icon on your navigation bar) or viewing your friends on your profile. To accept friend requests you just tap the icon next to their name/notification to add them.