She accidentally got her finger caught in the door.

Literal

She [topic-は] door [in-に] finger [object-を] [pinched-and-ended up-挟んでしまった].

挟む ('pinch, catch between, sandwich') is the everyday verb for things getting caught between two surfaces — fingers in doors, papers in books, bookmarks in pages. The auxiliary ~てしまう (here past ~てしまった) carries a distinctly regretful flavor when paired with mishaps: 'ended up doing X (which I wish hadn't happened).' Together they paint a small unfortunate moment with the resigned 'oh no' tone Japanese reserves for ~てしまう. The に on ドア marks the location where the catching happened.