Allen, this is such a broad question that could result in volumes of response in order to answer it. I know you posted this in the Coldwater forum, but I'll give my answers in general terms. Trout anglers do often talk about "matching the hatch" & that can apply to other species as well. However, often there may not be a "hatch". So, a bit of knowledge & experience may be required. I try to match the local forage. I don't often worry about exact matches, but do try to start with something of similar size & perhaps color, such as a baitfish, insect or crayfish, that may be found in the area. Being familiar with where you're fishing helps here.
As far as time of year, again some knowledge or past experiences can be valuable. But, if you lack such, then at least have a general idea. Google & other resources such as this site can provide good information provided you spend the time beforehand doing the research. The various hatches that trout anglers rely on can be predictable to some extent. Then, such things as terrestrials can be somewhat predictable. Obviously, you won't likely find grasshoppers in Dec, or even in early April in some areas, while they might be present year round in warmer parts of the country. Nymphs & various baitfishes are usually present year round, but again having a basic idea of what they may be, at least gets you started.
One other thing I do on waters I fish frequently & on new waters is spend some time looking around & paying attention to anything that might indicate where to start. At this time of year on some of the tidal rivers I fish for bass, carp are very active. They'll be moving around quite a bit & they make their presence quite known. I've found that bass will sometimes follow the carp, and take advantage of any meals that might get flushed from hiding by the carps movements. Of course I don't mind catching carp on a fly either, but this time of year they're in "love" & eating is the last thing they're interested in, so I don't waste the effort. In that case I might start with a streamer of a size & basic color that matches what is in those waters.
Picking a fly is usually a gut decision, based on what I've posted. Obviously, if you see insects, and a hatch, and have the appropriate flies, then that's an easy decision to make. If, not then you have to simply make a choice, and decide based on how you wish to fish. For me, I like topwater fishing the most & may start in that manner. Otherwise, I'll start with something else, often based on past experiences & successes.
I know this may not have answered your question, and you will likely get additional replies that give personal preferences for how others choose their flies. As I said when I started, your question is quite broad! I do hope this helped!