if you are in a Classic Realm (v1, v2 or v3Blitz), you need to go into menu Statistics/Allainces and select the Allaince you want to join ... not seeing the icon at the bottom of the screen means that you need to clean your internet cache (cookie problem)
if you are playing in New Realms (v4 and v4a), you need to contact the Leader, First Officer or Diplomat for them to send you an invitation to join in