Help me get better at Cycle Optomisation

So- I recently completed all the Puzzles in the actual game (I think none of them with Pistons, as I looked at them and went 'Those look too versatile, I think I'll have more fun not using them'.) I decided, because I definitely not addicted, to do all the puzzle again, this time at minimum cycles.

However, I've swiftly come to the conclusion that I don't actually get the principles behind minimising cycles. Can someone give me some advice?