I'm not sure there is a strict rule on this. I generally do this: 1)my opponent moves and presses his clock and I write down his move and think. 2)After a few minutes of fruitless thought, I make my move, press the clock and write down my move.
I used to write down my move, make it, an hit the clock, but I was told it was a violation of FIDE rules to write down your move before moving. This seems like an extremely stupid rule.
Linking the themes of chess clocks and move recording, on whose time do I record my move? Do I make a move, hit my clock, and then record a move, or do I record my own moves in my own time?