Welcome to the war! I'm probably having too much fun with this lately... but I guess not having a job does that to a person.
To join a kingdom, just go to the "Kingdoms" button on your left hand side and click it.
This will change the screen to display a list of all the kingdoms. Click the kingdom you want to join, and another list will show up that lists all of the factions within that kingdom. Sometimes the list is only one faction long, some times there are several factions within that one kingdom.
Under the list of factions within the Kingdom, there is a section called "diplomacy". Within this diplomacy sections, you can either "start a war" or "join" the kingdom.
Just out of curiosity, which faction are you?