She talked at length about her experiences abroad.

Literal

She [topic-は] foreign-country [of-の] experience [about-について] at-length spoke.

について is the go-to compound particle for 'about / concerning' a topic of discussion or study, and it's much more common in writing or careful speech than in casual chat. The phrase 長々と is a reduplicated adverb — Japanese loves doubling — meaning 'lengthily, on and on,' and the と attached to it is the adverbial と you see paired with mimetic and reduplicated words (ゆっくりと, きっぱりと, バタンと). Depending on tone, 長々と話す can be neutral ('spoke at length') or carry a hint that the listener found it a bit much; here the connotation depends on context.