Once you are in a guild there are two ways to leave. Exiled by a ranking officer or leave of your own accord. You must go to the "Guild Configuration" menu and click the "Leave Guild" button to try to quit your guild. You must select the button a second time to finalize the decision.

When exiled you will receive a system message informing you of your exile. I.e.;"Guildmember X has expelled you from the ranks of the Guildname X! ***WARNING*** You are NOT asked to confirm an exile.

Thanks to "Overkill" of Server 101 and his guild The Amazing RJ Fanclub for their assistance with some basic research.