The staircases are self explanatory. The red buttons turn on and off blocks that will travel up, down & diagonally.
I'm guessing that Daniel Hooper must have seen another puzzle app game called Monospace. See my review from about 4 years ago. In Monospace the room can be rotated from all 6 perspectives. It is a masterpiece. I've solved 59 out of the 60 levels. (Grrrr)
Back to Perspecto: right now I've completed 38 level and I'm stuck on #39. Altogether there are about 40 levels; Daniel's not sure. I really like Perspecto!