I started out by using the Ray Daniels approach of surveying some recipes of the same style for commonly used strains. From these initial recipes, I paired it down to a handful of strains to do specific styles. I ended up with one English strain, Scottish ale, American ale, Bavarian lager, and a strong Belgian strain.
I brewed extensively with those strains until I was pretty familiar which how they worked in my brewing. Then I moved to doing substitutes of each in recipes that I was repeating. I have expanded a bit in the strains I use, but I know how they will work for me fairly well.
I've changed my American strain from WY1056 to WY1272, which I find more versatile. I now use a couple of English strains to cover dry styles and maltier ones. I have expanded the amount of lagers I brew, so I now have two basic strains and have added a Czech pilsner strain which I use for several lighter styles. I've had worse luck with the Belgian strains and have stuck to the first one I picked. Meanwhile, as I stretched my brewing, I have also added a few specialty yeasts for those unique beers.
As several others have stated above, it comes down to looking at what others use, reading up on the yeast profiles to select the properties I want, and then repeated testing of a given strain to get to know it better.