Any Way and Anyway

Any way means by a choice of methods while anyway is an adverb meaning "regardless."

Examples:

Any way you slice it, we have to get out of here and we have to take him with us.

We're going to do it anyway!

Anyway also used to continue or resume the thread of a story or account example:

Anyway, we finally found a plumber who could come right over.

Source: The Wrong Word Dictionary (Dave Dowling, Ar-Risalah Product 2009), dictionary.reference.com