You need to pick your targets if you want to successfully catch carp on the fly with a level of regularity.
I generally ignore the following types of fish:
1. Suspended/neutral fish - these fish almost always produce zero action and waste time that could be spent on better targets.
2. sunbathers - if you see a carp laying almost motionless with its back out of the water, he has almost no interest in food.
3. Fleeing fish - if a fish is speeding away, he is spooked and will not hit anything.
I look for fish that are actively feeding
1. rooters - these fish are actively sucking up the bottom in search of food. These are prime targets and can be spotted by looking for plumes of mud clouds. Present a fly within a foot of him and he will eat it.
2. The up toppers - these are fish that are actively eating a clump of floating algae or insects off the top. For these, I like a fly called the devil bug or even a stimmie.
3. Jaws - it's hard to describe what this looks like but try to picture a big shark who is in obvious hunting mode. They are on the move but it's apparent that they are excited and looking for food. These carp are rare but when you find them, present a crayfish or even leech pattern to these guys and look for an aggressive strike. A great fly carper who goes by McTage (might even be on this site) calls them the "seek and destroy" carp.
Finally, when it comes to the hook set, it's all about either visibly seeing the fly go into that fish's mouth or gut instinct. The more you catch these things, the more you will understand the takes.
Here is a great blog post about the different behaviors and what fish to look for