Wild used to be locked for players in the “new player ranks” that started at rank 50 and extended through to 26. Ranks 25 - 1 were considered “regular ranks”, and you needed to be at least 25 to unlock wild.
However, as of April the ranking systems were completely overhauled. The “regular ranks” are now silver, bronze, gold, diamond, and platinum (all from 10 to 1). And the “new player ranks” are now renamed to “apprentice ranks”, starting at 40 and ranging to 1.
I would have assumed that you had to be out of apprentice ranks (in other words, at Bronze 10 or better) to unlock Wild. Your response to the link posted by Kazakus makes me doubt that.
Either way, once you are (1) at the minimum level required to unlock Wild, and (2) in the possession of at least one card that is Wild-only, you can mark decks you create as “Wild”, at which point you can use all cards in them, and queue those decks up for play in Wild mode.
I hope this helps.