Well, there are MANY different situations, and it's definitely not a one method fits all type thing. Unlike the previous poster, if it's a fertile stream, normal conditions, no fish showing on top, nymphing is almost always my first choice. But I will try anything. Go in with a plan, but be willing to abandon it quickly, use your instincts. It's hard to sum this up, heck, this whole board is largely devoted to figuring these situations out, and all of the most experienced guys argue about it.
One VERY important aspect for even reasonably fertile brown trout waters is timing. Fish that have more food available have the luxury of developing habits. They'll feed only at a certain time of day and spend the rest of day deep in cover. When they do eat, they won't move as far for food, and they'll be more selective. This puts more pressure on the angler. You could say it's tougher fishing, and in a way it is, though the flip side of that is that finding such streams and getting access is often much easier, as they're well known and publicized, access has been insured by the PFBC or other entities, and they even supplied nice parking areas without the hikes.
You've gotta be there when they wanna feed. If you find a surefire way to predict that, please let us all know!!!! It may be timed to hatches or other such events, I've definitely even see fish anticipate a hatch, where they'll come out into feeding lies and jockey for the best lane before it even begins. It could be an event, for instance rain often triggers some feeding activity. Could be time of day, i.e. the low light of evening, or the more comfortable water temps of morning in summer or afternoon in winter. The factors are endless.
As a general trend, the best time is mid-day through March and April, shifting towards evening till after dark in May and June, and then flipping to mornings mid summer. But there are plenty of exceptions to any such rule.
Then after you get the time right, you still gotta match what they're taking. Part of that is pattern. But a perhaps bigger part is figuring out whether they want it dead drifted, or movement, etc. If it's on top, is it in the film or floating high? If underneath, how does it wobble in the current, and at what depth? Are they focusing on it as it rises or falls? And even once you get all that, now you gotta make the proper cast.
Thankfully, fish aren't smart, and you can usually fool a few even if you only get some of those things right. Or perhaps they all aren't keyed in on exactly the same thing, so nomatter what we do we're bound to be right for a few. In any case, a good angler will usually get some, but an angler who figures out the proper keys for that time and place will get more.