You’ve gotten great advice. Take a look at those pics of flies and get a sense of the different types, “styles” of construction. Patterns names can be pretty confusing, some will tell you what they are designed to imitate (Pale Morning Dun, Blue Wing Olive), some will tell you what they’re made of (Elk Hair Caddis, Gold Ribbed Hares Ear, Pheasant Tail Nymph), some are named after people (Adams, Wulff), some sound like they’re named after someone’s mother-in-law (Rat Faced MacDougal) or have names like (Irresistible, Stimulator) that don’t tell you much. And many different patterns are designed to imitate the same thing (Mahogany Dun, Slate Drake, Dun Variant, White Gloved Howdy = Isonychia mayfly). And while you're looking up patterns, google "Tups Indispensible" and do some research on the origins of the name....
I’d bet your fly shop has already given you a good selection to cover most of the bases, and patterns that imitate a broad range of stuff that you should fish with confidence. He or she probably picked out some good all purpose dry flies like Wulffs or Trudes, Parachute Adams, Elk Hair Caddis or other great dry patterns. With those and some nymphs and buggers you’ll be off to a good start and can catch trout all over the country.
Assuming that you have trout flies, the main thing is to at least be able to identify the different categories- dry flies, wets, nymphs, streamers, and woolly buggers. Even if you can’t identify the exact pattern name, it’ll give you a lot of clues in how to fish it.
This is an index of good articles on basic presentations for dry flies and wet flies (including nymphs)
Basic Skills | Fly Fishing | Westfly
There are a bunch of different ways to group stuff, but here’s some things to look for based on how they’re constructed and what they’re designed to imitate. Some examples of fly patterns you may have:
Dry Flies- imitate adult mayflies (upright wings Adams, Blue Wing Olive), caddis (wings slanted back, Elk Hair Caddis), and stoneflies (real big ones like Stimulators, Salmon Flies), terrestrials (grasshoppers and ants) and “attractors” which don’t look like anything specific in nature, but are more “impressionistic” and have great fish catching powers, especially in fast water (Royal Wulff, Trude). Some different "styles" of dries:
‘Traditional” hackle- stiff hackle barbs balance the fly on it’s tip toes on the water, hackle is wound around the shank like an airplane propeller. Examples would be an Elk Hair Caddis, Adams, Blue Wing Olive (BWO). Pale Morning Dun (PMD). They’re good in water with some broken current to moderately fast water
Parachute- stiff hackle barbs, but wound around the wing post like a helicopter. The fly sits in the water film, and is good for slower water and picky fish. Examples would be a Parachute Adams, Parachute BWO, Parachute PMD etc.
Fast Water Dries- are heavily hackled, and float well in fast water and are easy to see. They can imitate specific insects or be more of an attractor type fly—or be a little of both. Flies like Stimulators which imitate stoneflies, can also catch when none are on the water. Wulffs which have upright wings suggest mayflies, and Trudes which have angled back wings suggest caddis and are good for riffles and other fast water stretches even when there is no insect activity going on.
There are other types of dry flies made with foam, stiff fine deer hair instead of hackle, (BWO Sparkle Dun, PMD Sparkle Dun. X Caddis) or other stuff, like feathers from the preen gland of ducks which have great flotation (called Cul de Canard or CDC and you'll see flies in catalogs like "CDC BWO", "CDC PMD" or "Elk and CDC") but the thing they have is that they’re designed to float. Most often dries are fished upstream. Look for foam lines, current seams, breaks in current around rocks, undercut banks etc.
Wet Flies are designed to be fished sub surface, and they usually have swept back soft hackle feathers. They can be divided into traditional wet flies, nymphs and other bigger stuff like streamers and buggers.
“Traditional wet flies” imitate drowned or emerging mayflies and caddis, and can be fished as general searching patterns. Soft Hackles like Partridge and Orange, and Sparkle Pupa are examples. Most often fished down and across stream, letting the fly swing in the current.
Nymphs imitate larval forms of mayflies, stoneflies and caddis. They can be tied with weight like lead wraps under the body, or with bead heads. Examples are Prince (for big mayfly and small stonefly nymphs), Pheasant Tail (thin mayfly nymphs), Gold Ribbed Hares Ear (fat mayfly nymph, cased caddis), Copper John and Brassie (cased caddis and other stuff). A bunch of different ways to fish them, including short line, under an indicator etc.
Streamers- imitate baitfish like minnows, alewife, sculpins etc. They can be tied with bucktail and or feathers. A popular example is Muddler Minnow (good for sculpins found in most trout streams) with a spun and clipped deer hair head. Also fished down and across, stripped through pools or you can “drop them back” downstream with pauses to let them hang in the current to fish good runs.
Woolly Buggers, again can be tied with weight, bead head etc. They sorta look like a lot of things like leeches, large stonefly, damsel fly or dragon fly nymphs and small minnows. They can be deadly. They should be easy to identify- marabou tail, chenille body and swept back hackle wound around the body. Great for lakes, deeper pools and fast runs. Fished like streamers.
So what do you use? Basically the best thing to do is to get some idea from a good fly shop in advance to know what to expect. Many rivers will have “Hatch Charts” on-line or you can get the from your local shop. They list the typical dates of emergence of different insects during the course of a season. Some of these charts go into a lot of detail and include recommended patterns and sizes, time of day the adults emerge, and where to look for them on a stream (riffle, slow water sections, muddy or rocky bottoms etc). Hatches in the same general area will often have similar hatches, and a lot of stuff is found all over the west. You don’t have to have exact matches for everything, but over time you’ll want to build up a collection of stuff that comes close to matching a broad selection of stuff for the major hatches in your area. A good way to go as you add to your collection is to choose imitative patterns based on a Hatch Chart or other info about local hatches that will build a range of sizes, some dark, some medium some light. It’ll increase your chances of having something that matches specific stuff on your streams, as well as having a shot at matching something unexpected.
Once you get to the water, look around on the water surface for rises, insects trapped in the film or riding along in the current. Look in spider webs, on the underside of leaves by the stream, and see if there is anything flying around near the tree line, like swallows swooping and diving that might be feeding on a swarm that’s about to hit the water to lay eggs. These are all good signs for dry flies Kick over some rocks and look for nymphs, or signs of cases and see if you can see what might be crawling around.
If you see stuff, try and match it with what you have. Look for a dry wet nymph etc that will fish in the right section of the water column, from there try and match it in size, then shade (light medium dark), then profile (may or caddis), then color. Don’t worry if it’s not exact, a basic assortment of patterns like Adams, Elk Hair Caddis, Pheasant Tail and Gold Ribbed Hares Ear. Prince Nymphs or other standards that your shop picked out will cover a lot of bases. Learning how to mend line to get a drag free drift in current is probably the single most important thing you can do to catch fish:
Fly Fishing, Fly Presentation, Mending - MidCurrent
As you get more and more into it, you can get as crazy as you want to. A good site to see pictures of different mayflies, caddis, and stoneflies and what they look like in their various life stages is Troutnut.com Fly Fishing for Trout
It’ll help give you an idea of what to look for on the stream, and you can compare pics to bugs listed on your Hatch Chart (or the advice you get from a local shop). For example, the Blue Wing Olive is a pattern that imitates a whole range of different mayflies, in various sizes that can be found all over the country. If you look at the nymph form though, you’ll see that it looks very close to a Pheasant Tail Nymph. And the final life stage, when it flies back to lay eggs on the water, looks like a Rusty Spinner. So, if you know that you should have a size 16 Blue Wing Olive emergence in the afternoon from your Hatch Chart, fishing a 16 Pheasant Tail Nymph (which looks like a lot of other mayfly nymphs too) in the morning, switching to a BWO dry in the afternoon, and a Rusty Spinner in the afternoon can be very productive. But then again you might have just as good a day with a 18 Adams…
Hope some of this helps.