。
She often sits there reading a book.
Literal
She [topic-は] there [at-に] sit [then-て] book [object-を] reading [thing-こと] [subject-が] often exists.
The frame ~ことがある describes occurrence in general — 'there are times when X happens'. Modify it with よく ('often') and you have 'X often happens'. The whole nominalized clause そこに座って本を読んでいる ('she is sitting there and reading a book') is the subject (marked by が) of ある ('exists'). The te-form 座って links the two simultaneous actions 'sit and read', and 読んでいる adds the ongoing aspect — she's not just reading once but in the state of reading. Idiomatically the sentence describes a recurring scene rather than a one-time event.