For those wanting some context for understanding the procedures and hand movements and more "detailed" hardware (including the way the aircraft interfaces with the catapult), I strongly recommend giving these two videos a view.
Obviously PLAN procedures would be a little bit different to that of the USN, but even from visible hardware and hand signals it seems like a lot of it is very understandably, very similar.
There are a surprising number of Youtube channels and videos which depict USN deckside procedures in a decent amount of detail