She was standing beside him.

Literal

She [topic-は] his [genitive-の] side [at-に] was-standing.

そば ('beside, near, by') is the everyday word for close proximity to a person or thing — slightly closer/more intimate than 近く ('nearby') or 横 ('next to / sideways'). Often appears in ~のそばに ('next to, by'). 立っていた is the past ~ていた form of 立つ ('stand'), marking the ongoing past state of standing. 立っている feels more durative than 立った ('stood up').