If a good state/county bike specific map is available, great. They can easily be found via an internet search, for example next door to me in Wisconsin I can use their bike maps either in printed form or online.
But some areas don't have good bike maps (right now, Minnesota hasn't updated its state bike map for over a decade, and even then it wasn't good). So what to do?
Now this is probably more than what some people are willing to do, but I look online at county maps from the state DOT to find out what minor roads are paved (these county maps almost always are downloadable). I also check out possibilities on Google street view to get a flavor of the area roads (where I can). But perhaps most important to me, I get traffic count information from the traffic count maps available on most state DOT websites. If a road doesn't have a decent shoulder, I look for roads with less than 1000 vehicles a day, and preferably less than 500.