Until recently I had only ever caught two carp besides a flyrod.....I can tell you that tailing carp are feeding, so if you get a wooly [censored] in front of them without scaring them by moving it toward them, you should catch one. When a carp sees a nymph, crawfish, helgramite, minnow, etc. close enough to catch, it will eat it. By making sure the carp sees it, then bringing it away (fleeing from) the carp may chase and eat it, otherwise it will scare the carp instead. You may catcharp on a floating fly as well. Use a catterpiller or mayfly imitation coasted overhead, and subtle twitching at the proper moment can induce a strike!
Good luck....its a lot of fun!!