Well we all know who is first, second, third and so on first because of the player rankings. As for the winning civ, well I guess it will come down to a personal and honest look at the nations at the (abrupt) end of the game, their techs, wonders, gold, total fame of the members, etc. and make a fair judgment on that.
There are these crazy quotes flying around how the head honcho wanted teamwork to act as a veil over inevitable "backstabbing" to make sure when the clock strikes 12 you have the most fame points, therefore "win". Well I like the people I am playing with, added a fair few to friends and play ciV with them. I don't plan on backstabbing these new interwebs friends. The thought of backstabbing people I've been playing with for a week or so just doesn't seem very nice.
Therefore in answer to your question, "How do you determine what civ win?" That's something you'll decide at the close of the game (and it only works if your honest
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Sorry it isn't a "Look here and see" answer, but the game wasn't designed to reward teams with a win, per se. Although a lot of people consider this, among other ways, of determining the winning TEAM. I hope you somewhat see where I'm coming from.
/Red