Crouch cancel grab is very important for puff. This technique is not talked about as much as it should be, I think. You hold down, then hit L or R (and hold), followed by A. Shield dropping is important as well. drill -> grab and drill -> rest (know when the flip will occur and when it will not).
For example, I love to shield vs marth. You have lots of options out of shield and you can make him scared to grab by threatening crouch rest a lot early on. But do that against a character like falcon and you're going to get stuck in shield and murdered.
I would like to point out that against a marth that knows what he's doing, shielding is very bad. Marth can get tipper f-smashes on puff if the grab connects. Marth's running grab will capture a crouching puff. Basically, crouch rest is not a legitimate threat. If it works against the marths you play against, go for it. but you are building bad habits which will haunt you when you play against a real marth. Vs marth i like to space sh bairs in neutral with very little time spent on the ground.
There is reading apart from parsing what has happened in the game so far. I think puff rewards reading the opponent's emotional/physical state. if an opponent seems sluggish and slow to react, empty hop grabs will likely be effective. If you can tell they want to be aggressive but know they cannot do so without leaving holes, know where their holes are and prepare to punish them. Punishing over-aggressive players with a setup into rest can be devastating for the opponent.
oh yeah and autocancel nair is god tier. look up the frames in the frame data guide.