As always, I could write a book on this topic.
Hate to be contrarian, but I've never had good look through the references channel. Too often I've had contractors get people they know for the reference.
Then my post gets worse from here...I don't have tried and true "best ways" to find someone good. After years of doing it and meeting a couple hundred contractors, I can just tell. I know, thats not helpful.
Look for little things. When they come to do the estimate and your describing the work, ask for their opinion. Be uncertain about something. "Im thinking about opening up this wall here, but am not sure if its load bearing, or if wires are running through it. Whaddya think?" If they say 'no problem, we can figure all that out', thats a bad sign. I like guys who'll go to the basement, look at the roof line, and check for outlets, then give me some detailed thoughts. Are they writing things down and measuring? Good sign. What kind of questions are they asking you? About the project, or payment schedule? If they start talking money too early, thats no-no for me.
If your job is small, this doesnt apply, but if its not, they should have worked on something big recently or better yet show you what they are working on now thats comparable in size. Drive there and check it out. Does the job site look like it was hit by a tornado? Small thing, but not good. Go there early one day. What time do the subs show up in the A.M.? Speaking of subs, guys doing decent size (but not huge) are likely to sub out electrical and plumbing. Find out how long (and confirm with the sub!) they've worked together. 7 years of history? Great sign. We just started together 2 months ago == not so great.
How does the bid look? Every book I've ever read says get labor/material broken out separately. I don't think I've ever had a contractor do this for any job bigger than a day or two worth of work. But I don't like when they turn in a lump sum bid with no breakdown. I like to see that they've assigned some value to individual parts of the job, and that value makes sense. Even if I have to give them some fake optional items to break out that Im not really considering doing. In my experience the better ones will sit down and price your job out while many of the rest will throw out a number and figure things out later (ie shortcut, hit you with change orders, or just overpriced it to start).
I know none of these are concrete, but my gut goes a long way in the process. But nothing for me is more important that meeting the contractor on the site and giving him every opportunity to show off his knowledge. Even if I know the answer to the question Im asking. Guys who really know what they are doing will be able to explain it to you so it makes sense. Others will BS their way through and you'll sense that.