That's fine except that the grammar police may point out that your pronoun does not agree with your antecedent. The singular "everyone" should pair with a singular possessive pronoun "his" or "her" whiich means that the grammatically correct way to write this sentence is "everyone has his own method". But even native speakers will make this grammar mistake and not think about it as It has become accepted practice to use "their" when gender is not known.

"Different strokes for different folks." "To each his own."

Without context, it's impossible to say. As a phrase, that is fine in some contexts - e.g. "How do you make flibbits?" "Well, everyone has the their own method. Some start with virgilidis, then...". Is that what you meant? Or were you trying to express something else? In most cases you would say "... method for (something)".

You could use the idiom: "There's more than one way to skin a cat." (yes, it's kind of a gross idiom, but it works) - but "everyone has his/her/their own method" is perfectly fine.

"Everyone's got their own way of doing things." - is how I would say it, personally.