It's easy to let the camera rotate around its own axis, but what if we don't want that - but instead want it to rotate around an object we selected, very much like a satelite orbiting around a planet.
- Create a new scene
- Add a plane (shift+a, mesh/plane) and scale it ("s").
- Add an "empty" (shift+a, empty) and move it to the origin (more or less)
- select the camera (right-click) and add the "empty" to the selection (shift+right-click)
- press "ctrl+p" to 'parent' them together.
- select the 'empty' and press "r, z" to turn it around - the camera will orbit around your "empty"