If the end of the prism has n sides, then the opposite ends of the prism have 2n edges between them. Each edge makes another edge when extruded into prism, making 2n+n=3n edges.
The ends have n vertices and so there are 2n vertices created by the two ends.
Each edge creates a rectangle in the prism, so there are n such rectangles and n faces plus the two ends' faces making n+2 faces.
In summary then, faces=n+2 (including the two ends); vertices=2n; edges=3n.