Learn French: Ensuite, tu sèches la frange le mieux possible. - Then, you dry the fringe the best possible.

Le mieux is the superlative form of the adverb bien (well). We use it to describe how an action is done, which in this case is the verb sèches (how you dry). Le meilleur is the superlative of the adjective bon (good) and is used to describe nouns (like saying "the best hairdryer").

How exactly does the phrase le mieux possible work?

It translates literally to "the best possible." Adding possible directly after a superlative like le mieux or le plus is the standard French way to say "as well as possible" or "as best as you can."

Wait, the dictionary verb is sécher (to dry) with an é. Why is it spelled sèches with an è here?

Sécher is a stem-changing verb. For the subjects je, tu, il/elle/on, and ils/elles, the accent changes from an acute é to a grave è to make the word easier to pronounce. It gives the vowel an open "eh" sound instead of a sharp "ay" sound.

Does la frange mean "fringe" like on a piece of clothing?

It can! However, in the context of drying hair, la frange refers to the hair cut across the forehead. In the UK, this is called a "fringe," but American English speakers will know this as "bangs."