Your Friends List includes players who have accepted your invitation to join your list and players whose invitations you've accepted.

One player must invite the other, and the invited player must accept the invitation before each player is added to the other player's Friends List.

You can see the status of other players that you have added to your Friends List. This tells you when you can join a friend's game session. If you want to join a game that a friend on your Friends List is already playing, you can either accept a game invitation from your friend or, depending on the game, you may be able to join your friend by selecting that friend on your Friends List and selecting Join.

You do not receive notifications when a Friend signs on during a game session. The only time that you will ever receive any kind of notification during a game session is when you receive an invitation from a friend to join that friend's game session. You have to check your Friends list to see which friends are currently signed in.