Carp are a great fly rod target, and everyone has posted some excellent information in this thread. Stick with this stuff and you'll be good to go man. I would add my three basic rules of carping:
1) Know your forage.
Carp can and do eat anything. There is no one magic fly that will work for all carp, but there is likely a magic fly that will work for your carp. Learn the forage and you will be good to go.
2) Don't cast until you can see the fish's head.
Detecting the take in MOST waters is the tricky part (again, this comes down to forage. Our here, I am lucky to get a fish to move 6 inches for a fly...in Lake MI I've seen them move 15 feet to SLAM a 2 inch long sculpin pattern). In general, this is a sight fishing game as Nick mentioned, so you better be able to see the head in order to see the take. I can count the number of carp I've "felt" on one hand out of my home waters (this goes up when I fish waters with different forage and more aggressive fish. So far I've caught carp in 8 states). I would rather spook a fish attempting a stalk, then cast when I can't see their head and miss the take.
3) You gotta make 'em move.
Carp are the most efficient feeders in fresh water and can suck a fly in from quite a distance away with little "tell." So my rule...make 'em move. I basically try to create a situation with my presentation where I am forcing the fish to turn its head to the side in order to eat. Then I set the hook when I see the head turn.
I am sure a lot of people will have a lot better advice, but those are my three rules. When I stick with those, I do ok...but don't for a second assume carp are easy. They can be predators, they can be grazers. They can key on a specific item, or they can be in the mood to eat just about anything. Combine this vastness in HOW they can feed with the fact that they have some of the best senses in the fishing world (let's not get started on their sense of smell or taste) and you have an extremely challenging fish. Then again, sometimes they are easy! Hah...you gotta love 'em.
For the scientific stuff that Nick mentioned, check out this podcast. Full disclaimer, I'm on the carp pro prostaff...mods, please delete if the link to the podcast is innappropriate.
Episode IV: CarpPro Flycast
Feel free to shoot me a message here or on facebook if you have any specific questions. And like Nick said...watch out! This is a slippery slope! I used to be a respectable angler!