What's the explicit description of the atlas of quotient stack?

Question

Let $U\to[U/G]$ be a quotient stack. How does one associate a $G$-torsor $P\to S$ and a equivariant map $P\to U$ to each $S\to U$?

Answer 1

For $S = U$ this is the trivial torsor $P = U \times G$, and for any other $S \to U$, this is its pullback, which is also the trivial torsor $P = S \times G$.