The main usage of this expression is essentially as the word 'like' (as in 'similar to'). For example: I touch-type (in) much the way my Dad does. I touch-type like my Dad does. Rather clunky examples, I'll admit, but rather weirdly, it's best illustrated by conflating them: I touch-type much like the way my Dad does(!) [in all honesty, the more I go over this example, the weirder it sounds...!] 'Much the way' is not very commonly used, whether in conversation or in prose, but it is considered (by some) a bit too colloquial to use in formal text (but not uniformly so, so you'll see it in general interest books and fiction, but again, not often).