、。
When she finished reading the book, she went out shopping.
Literal
Book [object-を] read-finish-[when-と], she [topic-は] shopping [purpose-に] went-out.
読み終える is a compound verb: 読む ('read') + 終える ('finish'). The ~終える/~終わる compound is productive: 書き終える ('finish writing'), 食べ終わる ('finish eating'). ~と conditional here means 'when/once' — once the finishing happened, the next action followed. 買い物に出かける ('go out for shopping') uses に as a purpose marker on a verb of motion.