It really is much simpler that it sounds. In a nutshell, carp have an extra line of bones sticking out sideways along the midline, so you just make an 'upper', and 'lower' fillet on each side, above and below the bone line. That's all there is to it. Oh, and dont forget to cut out the red 'mud line', which is actually the lateral line. It looks like flesh, but it is actually a super-sensitive sensory organ, composed of mechanico-receptive patches, or neuromasts, in a fluid-filled canal. It does many wonderful things, including sensing vibrations, sound, water composition and temperature, magnetic fields, helps the fish maintain it's spatial orientation so it can stay 'upright', and many other things. And carp have one of the most highly delevoped lateral lines of any fish. Unfortunately, it will make you sick if you eat it. Other species of fish depend more on other senses, such as direct sight, smell and sound to locate food, so their lateral line is not as large, or developed, and can be eaten with little or no consequence to the diner.
Carp are probably the best fish to smoke. It's almost like they were made for it. In my opinion, smoked carp is superior to any other smoked fish I have ever eaten, including salmon and trout. And carp makes some of the best croquets (fish patties) you will ever eat. They taste like a cross between really mild salmon croquets, and blue crab cakes.
Do you like Surimi (imitation crab meat)? Try this next time you get a large carp. Cut the fillets into 1-1/2" cubes and drop them in boiling water with shrimp powder and Old Bay Crab Boil. When they float, they are done. Instant surimi! Carp also makes excellent sushi.
Bon apetit.