。
She taught me how to write poetry.
Literal
She [topic-は] me [to-に] poetry's writing-method [object-を] taught [for me-てくれた].
書き方 ('how to write,' literally 'writing-way') is a productive compound: verb i-stem + 方 (かた, 'way/manner'). The same pattern gives 食べ方 (how to eat), 使い方 (how to use), 言い方 (how to say). It's the natural Japanese way to talk about manner or method — 詩の書き方 = 'poetry's writing-way' = 'how to write poems.' The auxiliary ~てくれる on 教える adds the warmth of 'as a favor for me.' Japan's poetic tradition is layered: 短歌 (tanka, 5-7-5-7-7 syllables) and 俳句 (haiku, 5-7-5) are the most famous, but free verse, modern poetry, and song lyrics all also fall under the umbrella of 詩.