I think carp get a bad rap here in the states. Everyone thinks of them as nothing more than a bottom feeding trash fish that destroy whatever water body they're introduced into. Thing is, that's a bum rap. When the carp were introduced to the states back in the 1800's, they were quickly stocked into the rivers that we poluted to the point that the only fish that could live in those waters were carp. So the carp got blamed for destroying the waters, when in fact it was us that did it. The other reason the carp were brought over was so that the immigrants would have a familiar fish, which grew big and produced pretty well. The carp provided sport and food.
The fact is the carp will thrive pretty much anywhere they're introduced, so long as the water is deep enough not to winter kill. They can tolerate very high water temps - 80+ degrees will put them off feeding, but they'll still be alive when the water temps cool.
Carp are omnivores - just like us. They eat plants and animals - I've watched many occasions while a
pack of huge carp chased around schools of baitfish, ravaging them. Those same fish a while later would gently, slowly work their way along hte surface sucking down clumps of floating grass, berries that'd fallen into the water, and seeds that blew off the grass fields near by. Very adaptive fish.
They're also smarter than we Americans give them credit for. Carp have very, very sensitive mouths and senses of taste and smell. They quickly learn to associate certain tastes/smells/textures with good or bad experiences. Say you catch & release a carp using a red pom pom (little fuzzy ball) impregnated with scent. That carp will then tend to associate the color red with being caught and released, and will shy away from anything red. They'll be suspect of that particular scent also. They will be more cautious when mouthing the bait, and they learn to feel what the hook feels like and will almost instantly spit a hook if detected. That's one reason I use the Gamakatsu Octopus style hooks - like we use for salmon and steelhead in these parts - for carp fishing. The hook does not have a very long shank, and it allows you to completely envelop the hook and shank in your bait, while leaving a good bite-sized package for the carp.
If you find carp in cold, clean water - say the same kind of water you'd find trout or smallmouth bass in - the carp will be much cleaner tasting than those taken from warm, muddy water, and are much more fit to eat than their warm, muddy water cousins.
The way I fish for carp also provides the most sport, I think, of any conventional rod & reel method (this doesn't include fly fishing, which is hella fun also, but I'm talking about conventional tackle not fly tackle here.)
My carp setup:
7' light or ultra-light action spinning rod, rated either 2-6lb test, or 4-8lb line
Shimano spinning reel, in the 2000 or 4000 size class, depending on the rod and the water to be fished
4lb Berkley line
Gamakatsu or Eagle Claw (Gami's are better) octopus style hook. I normally fish a size 4, but if the water is very clear or if the fish are very light biting, I go down to a size 6. Occasionally if targeting really big fish, I bump it to a number 2.
1 or 2 "Corkie drifter" drift-bobbers and a toothpick.
Sandwhich bread - usually wheat, or some multigrain, or whatever is handy and cheap. Usually don't use plain white bread though. The fish tend to prefer wheat/whole grain/multigrain stuff.
Anyone familiar with fishing for salmon or steelhead in the PNW or Alaska will know what a Corkie Drifter is. For those not around here, corkies are a small foam sphere, with a hole bored through it to allow it to be slipped onto the line. They're brightly painted and come in dozens of color patterns. They were originally intended for salmon/steelhead fishing, where they're slipped onto the line immediately above the hook, and they snug up to the hook when you're drift-fishing (casting upstream and letting the line dead-drift downstream) and help keep the hook/bait off the bottom. The way
I use the corkies for carp fishing is different - I use them for my bobber/strike indicator. Depending on the size of the hook/bait I'm using, I will slide one or two of the large-size corkies onto my line, adjusting for water depth (around here I never have to set the bobbers more than 5 feet above the hook, as the water is usually maybe 4' deep at the max where the carp are found). The corkie(s) is then pegged in place by a round toothpick jammed into the hole and cut off leaving just a little sticking out in case I want to adjust the depth. To adjust depth, pull the toothpick out, slide the corkie where you want it, then jam the toothpick back in place. Simple, easy, very effective.
Now it's simply a matter of baiting the hook and starting to fish. I tear off a hunk of the bread, getting a piece of the crust with it. I impale the crust with the hook, then simply press the whole mess of bread around the hook, turning the hook/bait in my hand with each press, pressing as hard as I can, forming a kind of double ended pyramid of compressed bread around the hook. This compressed bread ball sinks, eliminating the need for additional weight (I'll talk more of this in a minute.) Getting the bread really compacted around the hook is key here - if it's too loose, the bread will come off on the cast, or will just simply unravel itself and come off or be easily torn off by fish in the water. A good compressed bread ball will stay for many, many casts, or until a fish is hooked or pulls the bait off.
When I fish for carp, I stalk them. That is to stay, I look for signs of feeding fish unless I'm fishing a spot I
know always holds fish. I look for them in water that is generally no more than 3-4 foot deep, is generally weed free or very little weeds (thick matted vegetation is not good for this type of fishing), and where fish are feeding within 30 feet of the bank. Pretty easy to find carp in places like this. Tell tale signs of feeding fish are strings of bubbles, v-shaped wakes, and trails of silt as the fish stir up the bottom if feeding on the bottom. In shallow water they tail just like bonefish.
Now casting the unweighted corkie (very light) with the bread/hook combo is where light tackle shines. You don't need lead, and in fact don't WANT lead on your line when fishing for carp. You only need to usually cast out 20 feet or less. The fish will pick up the smell of the bait and come in closer if they're further out. Adding lead to get further casts won't do you any favors here, but will in fact cause fewer hookups, because when a carp takes a bait, they don't simply grab and swallow. They pick the bait up and swim off a ways before swallowing the food. As soon as the fish mouths the bait and starts to swim, they'll feel the resistance of the lead and drop the bait. In other words, you have to set the hook almost as soon as the fish starts biting or stand a good chance of them spitting the bait.
The corkie drift bobber also shines here, because it it has very little resistance on the fish's end, as it's small and light. When a carp picks up the bait, the bobber will start moving off after bobbing once or twice. When the fish starts swimming off is when you want to set the hook. A larger, traditional bobber would again add too much resistance, the fish would feel, and would cause spit baits.
Long, light action limber spinning rods with the light 4lb line really let the fish show off it's stuff, but also help tire the fish quickly because they're fighting that limber spinning rod. A lot more fun than just dragging the fish in on some heavy fight-deadening rod with 20 or 30lb line. If your drag is set properly, you'll almost never break off a fish either.
Average carp in the waters I fish is 5-10lbs, but the largest I've caught has been a hair over 20lbs. Did that on a 6'6" spin rod with 4lb line. Fight lasted a bit over half an hour, and I almost got spooled twice

Did land and release the fish though. One of these days I want to get a 30lb fish on 4lb line.