。
She reached into her handbag, looking for her ring.
Literal
She [topic-は] handbag [in-に] hand [object-を] put-and ring [object-を] searched-for.
手を入れる ('to put one's hand in, reach inside') is a vivid expression — your hand is the object, the inside-place takes に. The compound action of reaching-and-searching is sequenced with the te-form: 手を入れて、さがした. The verb 探す, written here in kana さがす, is a routine kana spelling for this everyday verb; learners often see it written 探す with the kanji, but the kana version is widespread in casual prose and signage.