Anarchism isn’t no rules it’s no rulers. Even newbie anarchists will be able to tell you that absent a structure making power accountable to the people, power will just emerge in an unaccountable form.
Anarchia Island would probably just govern itself as a direct democracy with a heavy emphasis on equitable management of resources and regular attendance of public meetings to decide any pressing matters.
Picture the way New England townships will sometimes run themselves with everyone coming to the town hall meeting and hand voting on the questions of the meeting and you can begin to get a basic idea what it’d look like.
Some very ideological anarchists might insist that the decision making process would involve consensus democracy which is just a whole other can of worms that isn’t really worth delving into beyond mentioning that the Inuit nation apparently makes it work in Nunavut so it’s not completely crazy if you’re hyped enough for it.