Lord Flash Fire is running it so he may institute his own changes, but when I've done it in the past (only a few times, mind you,) each player has their own deck and you report which cards you have and what you draw. Then Flash Fire will report what happens during the villain and environment turns, afterwards we take our turns.
So unless something drastic happens or as a team we discuss going in a different direction my first turn might look like this:
Golem Unity (25 Hp)
Hand: Volatile Parts, Stealth Bot, Modular Workbench, Hasty Augmentation
Cards in play: None
Start of turn: Nothing
Play: Volatile Parts
Power: Unity deals herself 4 energy damage (21Hp) and puts Stealh Bot (5HP) into play.
Draw: Bee Bot
End of turn: Nothing
Hand: Modular Workbench, Bee Bot, Hasty Augmentation, Untiy (21), Stealth Bot (5)
Then I might put a note like: Redirect any hits of 1 damage to Stealth Bot, otherwise don't.
It's pretty simple, and a lot of fun.