Unfortunately, the answer to your question involves quite a bit of non-canon material included in the EU. To my knowledge, non the of the known canon sources address this problem. However, if you are satisfied with non-canon answers, I can try to answer this for you.
Mandalore was the Basic transliteration of the title used by the the supreme leader of the Mandalorian people and culture. In its truest, native rendering as Mand'alor, the title meant "sole ruler" in the Mandalorian language of Mando'a. Originating with Mandalore the First, the mythic leader of the Taung warriors who went on to become the first Mandalorians, Mand'alor became the title passed down for use by the subsequent leaders of the people for generations after. Functioning as a combination of both king and warrior general, the Mand'alor was the closest to a head of state the wide-spread Mandalorian clans possessed, and in addition to holding the secondary title of Al'Ori'Ramikade—"Commander of Supercommandos"—Mand'alor was the de facto ruler of the Mandalorians' conquered home planet, the eponymous Outer Rim world of Mandalore. Outsiders to the Mandalorian culture often respectfully addressed the Mandalorian leader as Lord Mandalore. The importance of the Mand'alor was reflected in the six tenets that outlined Mandalorian culture, the Resol'nare, one of which dictated that a Mandalorian rally to the Mand'alor when called upon.
For years, the position of Mand'alor was traditionally symbolized by
the passing of the mask of Mandalore upon the death of the previous
owner, but in later times this custom had faded into antiquity, and
new Mandalores needed only the support of the people to ascend to the
role. Numerous Mandalores also took to adapting descriptive epithets,
in order to distinguish themselves from those who came before and
after. Following the foundation of the New Mandalorians, the pacifist
sect rejected the authority of the clan-chosen Mandalores, and instead
appointed their own leaders in opposition to those who ruled the
warrior clans. The Death Watch, in turn, appointed their own Secret
Mandalores in opposition to both the New Mandalorians and the
unaffiliated warrior clans. During this period of social division in
the Mandalorian culture, the traditionally chosen Mand'alor of the
clans became known as the "True Mandalore," as a means of countering
the claims of the New Mandalorian and Death Watch leaders. Throughout
the history of the galaxy, at least twenty-one Mandalorians declared
themselves Mand'alor, and met with varied degrees of success in their
attempts to lead the Mandalorian people.
Essentially, it passed upon the death of the old Mandalore (Mand'alor). Usually this was a passing with a direct confrontation between the old and the new, but there were occasions when it was passed willingly. I.E. when Fenn Shysa died, he passed it Boba Fett, both out the need to maintain the old traditions and sense of hierarchy, but also because he believed Fett to be the true successor to Mand'alor (which was in turn a throwback to the original comics in which I believe Jango Fett was Mandalore himself, though don't quote me on that.)