Basically you start the combat by attacking someone, be it by shooting/meleeing them and so on, this gives all the UI and stuff. That starts the combat, where there will be a timer which counts down to combat start, where the attacker is able to tag in other people, say a group of rebels running away. On combat start, the attacker gets the advantage to do their thing first and then the other person goes until the fight is over, either from no one attacking for a few rounds (I think 3 or 5) or the people in the fight end it themselves by a vote system which is just 1 button, or obviously by there being no one and nothing left to fight if just one person is left.
For people entering, if they attack someone in TBC already they're slotted in for next round after the current rounds active player or at the end of next round. The latter is the same for people who are brought in from a "tag" which is just someone in TBC damaging someone outside of TBC, and unless they're attacked while in TBC, they'll be at the end of the round for their turn. I think this is how it works anyway. The damage dealt from initiating TBC or tagging people isn't persistent, and I think ammo resets as-well. Also, whether it's your turn or not, you're able to crouch.
As for what it looks like from the outside, I don't really think it'd be weird, it's the same as RP'ed TBC, except without the arguments and accusations of powergaming and whatnot, and obviously quicker as you're not waiting for anyone to type anything, just get going.
Edit: Oh and in the video from Adam, you see that when combat starts the NPC's go first even though Adam attacked them first. This is because NPC's always take the first turn regardless of who starts combat whether it's them or players
