Most of us fly anglers learn from a mixture of books, videos, & other anglers. There are many books about the bugs a fly angler needs to know & asking a more experienced angler who is willing to help can really shorten your learning curve. Hiring a guide can be another great resource, but since most of us don't always have a guide with us (especially on local waters) we'll have to do most of the bug-detective work ourselves; and yes- entomology is mostly detective work, as it applies to us fly fishers.
That's part of the fun anyway, trying to figure out which fly to use. If you're just getting into this part of the sport - the entomology - how do you decide which fly is best to use when a good hatch is on? Unless the beginner is armed with a specific fly for a specific hatch they usually end up tossing either a generalized pattern (hare's ear, pheasant tail nymph, adams, etc) or some kind of attractor pattern. They're then left to rely on their abilities to manipulate fly & line for success. I call this the "cast & hope" method & there's nothing wrong with it. It's what we all do when there is no hatch happening. But when a certain type of bug is coming off the water in great numbers, we're going to want to take advantage of the situation.
After experiencing enough hatches on local waters that they aren't prepared for, an angler is going to start wanting to get into the action by matching hatch. If they can do this on a fly they've tied &/or designed themselves, then it won't be long before the "desire" morphs into an "obsession".
So how do you begin figuring out these hatches for yourself? Well, understand that it might not happen quickly. Depending on the duration of the hatch, it might take you until next season before you can prove your theories. That can be a little maddening, but as you well know, patience is the key to success in angling. So while there are several ways to figure out mayfly & caddis hatches, here are some basic procedures:
1.) Pick ONE -& only one - of your local hatches that the trout feed on predominately when those insects are on the water.
2.) Study that insect very intensely. This usually means catching specimens of the dun, mature adult, & nymph or larva & pupa.
3.) Going to the tying vise & either inventing a pattern to copy that insect exactly or modifying an existing pattern to better copy your local bug.
Now, all that sounds great, but how do you actually execute those procedures above? In all reality, it's not quite as easy as I made it sound. There are some fly fishing entomology books that will help guide you. I would avoid delving into any really technical college text books on the entomology, unless that's your cup-'o-tea, because this stuff can get pretty confusing & entomology is a huge field of study. We're only looking at a very small part of it, as it pertains to the bugs our fish eat. Add to that the discipline it takes to do this. You're going to be spending time with a net in your hand trying to catch bugs, or turning over rocks from the stream bed while other anglers have their lines in the water. Trust me, that discipline will be well rewarded in the future.
So here are some pointers to get you started:
-Start with an easily identified hatch. Ideally, it would be one that's on the water when nothing else that looks like it is, too. For example, you might locally have a green drake hatch that is physically bigger than any other local hatches; or maybe, like me, you have a heavy local white fly hatch that, because of it's distinct color, can't possibly be confused with any other bug. Your local hatch charts might be of help here, too.
-When the hatch that you've chosen to study is on the water, take time to just sit & watch it. Don't fish, only observe - at least part of the time. After you've studied the bug's natural behavior, try to catch a specimen. Ideally you'd take this specimen home with you, but taking a very detailed photo will also work, if you have the knowledge & skills to take good macro shots.
-Armed with the example you took from the stream (or a really good set of photos), head to your tying vise & get creative. You might need to make up several different patterns to try. Get back to the water while the hatch is still on & see how your new flies work. If not, maybe take some more samples or photos & try it all again until you get it. This process may very well stretch into the next fishing season, so be patient.
In fly fishing, nothing trumps local knowledge of the water you're fishing. By methodically learning to match a single hatch you'll be expanding your knowledge of the sport & the water you fish. After you've learned one hatch inside & out, you can then move onto the others in the same way. This will be a multiple-year commitment on your part, but it's well worth it. I promise you that, as a fly angler, nothing will bring you more satisfaction & reward than when you match the hatch, catching trout on a fly of your own design that you created by studying the natural insect.