Recently I encountered the situation where I needed to switch GC's to be able to compete in frontlines with my FC, and while I was looking for info on this I found very little real help. So in an attempt to help others who may be in my situation I thought I'd provide a brief overview of what it actually takes to change from one GC to the next.
The first step if you haven't taken the time to rank up in your current GC you will have to do this first. It is required that you be a second leuitenant in your current GC before you are able to change allegiance. To do this you must accumulate the appropriate amount of guild seals for each promotion as well as complete up to the second page in your GC hunting log as well as complete multiple quests for promotion. These quests are generally go to this dungeon talk to this person outside and then complete the dungeon through the duty finder.
Once you have reached the rank of Second lieutenant all that is left is to go to the GC hall that you wish to join. You will speak to the NPC to switch your allegiance an then you will be the lowest rank of this GC. Some noteworthy things that then occur are any boarding or equipment you have earned with seals from your former GC will no longer be able to be used. A basic boarding of your new GC is available on your companions tab however. I do not know if you are able to use former GC hear as a glamour option or not as of this point.
I hope this may help any who were stuck at the same point I was and if you have any information to add it is always appreciated.