Trading a car in that I still owe on?

I've read that you CAN trade in a car you still owe money on. However sometimes it's not a great idea. So here is my scenario and questions.

I recently (January 2015) bought a 2015 Ford Fiesta for $16500. It has less that 10k miles on it right now. I want to "upgrade" more or less to a bigger vehicle.

Is this possible with a trade in? Or do I have to pay off the Fiesta?

I've heard the term "upside down". Can someone explain this and how to avoid it please.

How does your credit score effect the ability to trade it in?

The trade in vehicle does NOT count as a down payment, but how does it help lower the cost of the other vehicle? Anything other than the fact that you're " trading " and they aren't losing all of the money (kind of like collateral).

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