。
She took the tablecloth to the dry cleaner's.
Literal
She [topic-は] tablecloth [object-を] cleaner-shop [as far as-まで] [carried-and-went-持って行った].
持って行く is one of the most basic compound motion verbs in Japanese: 持って (te-form of 持つ, 'hold/carry') + 行く ('go') = 'take' (= carry-and-go). Its reverse, 持って来る ('bring,' carry-and-come), encodes direction relative to the speaker. The まで particle here marks 'as far as / all the way to,' emphasizing the trip's destination as the final point. クリーニング店 is a 和製英語 (Japanese-coined English) compound — English 'cleaning' rendered in katakana, plus the native 店 ('shop') as a head noun.