。
She showed me how to use the hair dryer.
Literal
She [topic-は] hair-dryer's use-method [object-を] me [to-に] explaining gave-for-me.
使い方 ('way of using, how to use') is built from the verb stem 使い + 方 (the suffix 'way of doing'), one of Japanese's most productive nominalizers — 食べ方 ('way of eating'), 行き方 ('way to get there'), 考え方 ('way of thinking'). 説明してくれた combines 説明する ('explain') with the benefactive ~てくれる, marking the explanation as a favor done for the speaker. Without ~てくれる the sentence would still be grammatical but would lose the gratitude inherent in the framing.