I am certainly no expert, but I learned a few things in the last few days, so I can offer what I found so far.
Carp are wily. As mentioned, they will inspect and exhale bait offering very quickly, so they are extremely difficult to catch with a simple bait-on-hook scenario as an angler will very likely not be able to react quickly enough at the first nibble to set a hook. Also, they are sensitive and suspicious to any line tension as they pick up the bait and will reject it at that point. And once the bait is rejected, it will apparently not be revisited by the same fish.
As a result, the aforementioned hair rig is the setup of choice (google.com is your friend here) as the bait is threaded onto a line extended away form the hook and it allows the fish to inspect the bait, sans hook; leaving the bail open on a spin reel negates any feeling of line tension. Then, the fish will begin to devour the bait and the hook will follow. Once the hook is encountered, the fish was already commited and the hook will more likely catch before it can be ejected. At the point the fish feels the hook prick, it will likely spook a bit and move away. You will then see your line start to spool out.
Some people use what's called a bolt rig that has a heavier weight (like 2-3 oz.) with a stop that will partially set the hook when the fish 'bolts'. I opted to just grab the line with my hand for a brief second and let go (very briefly so as not to inadvertently break my light tackle...this happened once when I held on too long). I also went to a size 1 hook, from a larger one because I was just getting a bunch of stolen bait and no hookups with a larger size...the smaller size got me much better success with actually getting a hook to reach the mouth and stay in. Yesterday, I hooked 5 in this manner, but what I later determined to be a too-high drag setting caused me to lose some. When I lightened my drag up, I finally netted a 30" carp.
For bait, I rolled some wheat bread into balls with a mixture of ground nuts and blackberry syrup (the kind used for lattes). I added a few bits of corn after threading on the bread ball; the carp really seemed to like it.