Been a moderator on one soccer forum, and administrator of my own political forum (which I later cancelled as far-right members ruined the forum with racist outings on constant basis)
In the end, you get moderator if you have been involved long enough and posted on frequent basis, been online very often, and reached a respectable number of posts that actually added value to the forum (= no spam posts or short posts, but reaching a fair number of posts while actually only posting valuable posts)
In the end it is the decision of the admins and usually they will put announcements when extra staff is needed. At least that is how many forums do it, at my own political forum as well we would not consider spontaneous applications but posted a vacancy whenever an extra moderator was considered necessary.
May I add: think well before you start. Moderating means you are expected to be online frequently, it can be a duty that takes several hours a week. On my political forum and the soccer forum where I was moderator, I spent about 2 to sometimes 3 hours a day. It can be a lot of work to read throughout all posts, you cannot skip a lot of topics because the mods have to keep an eye on a discussion even if the topics is not interesting to them.
So it is great if people show determination, but consider this well before just applying.
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Do what Thou wilt shal be the whole of the Law.
Love is the Law, Love under Will. And...
every man and every woman is a star
(excerpt from The Book of the Law - Aleister Crowley)
"Od lo avda tikvateinu" (excerpt from the Israeli hymn)