the way one talks; one's way of speaking
Refers to a person's manner of speaking, often implying tone, politeness, or choice of words.
He has a rough way of talking.
Teach how to speak to superiors.
話し方 is a more general term for 'way of speaking' or 'speech style', while 口の利き方 often carries a nuance about the appropriateness or tone of one's speech, especially in social contexts.
Standard kanji spelling.
Common mixed kana-kanji spelling.
Alternate kanji for きく; less common.
Compound of 口 (mouth) + の (possessive particle) + 利き方 (way of using/working), from 利く (to be effective, to function). The phrase literally means 'the way one's mouth works', referring to one's manner of speaking.