。
She had a sad-looking face while reading the letter.
Literal
She [topic-は] that letter [object-を] was-reading [time-とき] sad-looking face was.
Past progressive ~ていた combined with とき ('when') describes the duration during which the action was happening — 'while she was reading.' 悲しそうな is the attributive form of the visual evidential ~そう ('looking sad'), modifying 顔 ('face'): 'a sad-looking face.' The whole describes appearance from outside, the sort of detail a third-party narrator would notice and report.