。
She's been living with us since last summer.
Literal
She [topic-は] this-time-before [genitive-の] summer [from-から] us [together-with-といっしょに] is-living.
といっしょに ('together with') is a stock comitative phrase combining と ('with') + いっしょ ('together') + に (adverbial). It's slightly more emphatic than plain と alone, foregrounding the shared activity. 住んでいる ('lives in') uses ~ている for the resultant state of taking up residence — the same pattern as everyday 'live in' expressions. から ('from, since') sets the time anchor. A warm, domestic sentence implying co-living arrangements, the kind that would describe a family member, a homestay student, or a close friend who's moved in.