After selecting the chatter's name, click "Friend request" to send a request to the other person. Until they accept, they will appear gray in your friends list. Friends list can be accessed from the right user panel by clicking the "friends" tab at the top. (If you don't see this you are not logged in as a registered user)
A green dot means they are online, A red dot means they are offline To remove a friend from your friends list, click their name and choose "Remove friend". You can't add a guest as a friend (they don't have an account).