She dried her hair well with a towel.

Literal

She [topic-は] hair [object-を] towel [with-で] well wiped.

タオル is a katakana loanword from English 'towel.' で marks the instrument. 拭く is 'to wipe / dry by wiping.' よく ('well, thoroughly') is the adverbial form of いい/良い ('good') — note the irregular adverb stem 良く.