Most people fish with bread/corn etc, but they'll take nightcrawlers too. They eat pretty much what they can get a grip on.
I just decided to try carp fishing this year, and I found this site:
Wild Carp Club of New England | Wild Carp Club | Wild Carp Companies, Baldwinsville NY
They're having a tournament over the year, and this Sunday, May 14, they're meeting at Brookline reservoir. I'll probably join them and try to learn from the carp-sharpies. Everyone wants to catch the biggest fish possible - why not just target the biggest fresh-water species?