how do i catch one, and how do you identify them?

As for catching one.A bait and cage trap maybey?

correct me if im wrong, but arent they extinct?

They aren't extinct. The "carrier pigeon" is the same species of pigeon you see flying around the city. I've always wanted to catch a few and breed them. With some selective breeding, you could sell them to carrier pigeon hobbyists for $40-$70 each. As for catching them, you could get a pellet gun and outfit it with some tranquilizers.

You're thinking of the Passenger Pigeon.

Right, and they'll be impervious from the fall out of the sky.