'Exactly how' is the best choice for me, though 'the exact way' has nothing against it except that it might refer to the method (they put on their togas before they put on their sandals). 'The exact way how' is indeed poor style, but it is common English in casual conversation, and that is what much of the internet is. Though googling is a reasonable (though sometimes incautious) method for determing basic use, it is not a source of good style.
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