[warning: under construction, this method no longer works!]
..Leaving your guild is as easy as shown in the screenshot. Hopping to another guild has 2 methods though, and because of these methods it is easy to leave your guild, hop to another guild (to collect wood and iron, or join a fresh guild battle on Tuesday, to donate and collect on 100v prizes, several reasons), then hop right back to your home guild, avoiding the 36 hour cooldown between joining guilds altogether.
The first step is to leave your guild. If you don't leave your guild you will be unable to send requests to join another guild. You will be able to receive invitations to join another guild but if you accept and you are already in another guild the invitation will fail.
RTJ or request to join is done by going to the target guild's home page. The easiest way is to get a direct link from your list of guilds but if you do not have a list you can visit the keep of any member of the target guild and copy the link from their keep page, as well as clicking on the link to go to the target guild's home page.
ITJ or invitation to join is done by getting an officer in the target guild to go to the guild management page, enter YOUR army code in the invitation box, and hitting the button to send the invitation.
The second step while you have just left your home guild is to RTJ your target guild(s) (there can be multiple target guilds to hop to in a session). Be sure while you have not joined any guild yet (and are out of 36 hour cooldown) you send ALL your RTJ's as you will not be able to send an RTJ while inside the 36 hour cooldown. 36 hour cooldown the moment you join any guild. ITJ's will only work if you are outside of 36 hour cooldown, so don't use ITJ's.
The third step is to RTJ your home guild (the guild you just left). This step is crucial and must be done BEFORE you join any of your target guilds to avoid 36 hour cooldown.
The fourth step is to actually hop to your target guilds. A guild officer in your target guild must go to the management page and click 'accept' on your RTJ for you to join, so you must coordinate with the target guild officer to do this for you. Once you are accepted 36 hour cooldown starts, but you will be able to conduct your business as a member of that target guild. Done joining that ouroboros? Leave the target guild. Contact your next target guild and officer of that guild to let you in by clicking 'accept' on your RTJ. And so on.
The fifth and final step is to leave your last target guild and hop back to your home guild, where you contact an officer of your home guild to let you back in by clicking 'accept' on your RTJ from the guild management page.
Some things to remember is that in order to actually send a request to join a guild is that you yourself must not be inside a guild and that your target guild must have space for you, have less than 100 members. If an officer clicks 'accept' on an RTJ and there is no space the RTJ will fail and DISAPPEAR!
In order to manipulate the guild average level by booting members of the guild before summoning conquest monsters, each booted member is free to rejoin the guild assuming the are outside 36 hour cooldown. In addition, if each member sends an RTJ and receives an ITJ, they are able to rejoin with either method, assuming they start outside of 36 hour cooldown. So boot members, summon, have them immediately rejoin.
Hope this helps all of you out there defeat the forces of the castle age forums!