umm, how do you contact someone in another alliance to actually get an invite? I'm I missing something ingame?
Invite Only is a little misleading, you aren't actually invited, you request to join.
When you click 'Join' in an Invite Only alliance, a message appears in the Alliance Chat with the message you wrote and your in-game name. Council, Co-Leaders and the Leader can either accept your request or decline. The message will dissapear if you leave the alliance page, so you'll have to wait if there's no one to accept it right away.