I have been responsible for hiring all the instructors at my music school Starland Music Center for 30 years. I'll share with you what I've learned over the years what I consider to be the best ways to separate the "wheat from the chaff." 

Teaching with a plan 

The best teachers always prepare and have a plan: it's said in teaching that for every hour of teaching you need to prepare twice as much. You should be able to tell whether you're dealing with a professional just with your first meeting - they will determine where you are, where you are trying to go and then propose a method for getting you there. Even in the first lesson they might give you exercises to evaluate where you are. 

The best teachers are not afraid to tell you their methods. 

You can always tell the worst teachers, because they are the ones who "wing it." If you can tell that your prospective teacher hasn't prepared for the lesson and looks like they are making up stuff on the spot - they probably are. Get away as fast as you can. With these types of teachers you won't achieve any progress, because there's no system to their teaching. If you don't realize this right from the beginning, you end up six months later feeling like you haven't progressed at all and you become very confused. You may even blame your lack of progress on some ridiculous notion that "you don't have any talent." 

The best teachers stick to their plans and while they may reward you now and then by teaching you a song you really like, more likely they will find out anyway your tastes and incorporate those into later lessons when you get to that level. 

Travel distance 

How to find a good teacher also depends on how far you are willing to travel for your lessons. The more consistent you are in not missing your lessons the faster you will progress - and it's much easier to be consistent if you don't have to travel too far to see your teacher. 30 minutes travel time is a good average, but only you know what you can honestly tolerate. 

Abilities vs. teaching skills 

The two are not mutual (but neither are they mutually exclusive). Just because a guitarist is an amazing performer, does not mean that they could be a great teacher. In fact, it's more likely that the best teachers are the ones who are unable to perform so much because they are teaching so much. When you are a beginner, it's best to go with a teacher who is excellent at teaching you all the basics, you don't need to worry too much about how great a performer they are. But then as you advance, you can always seek out another teacher who specializes in a particular style that you like. 

What you should be looking for is a teacher who is both an inspiration and someone who has traveled the hard road of being a student and comes back to show you the way. 

Instructor experience 

1) One way to work out whether your prospective teacher has enough experience is to see how many students they teach. If it's true that it takes thousands of hours to learn to play an instrument, then it's also true that it takes thousands of hours to learn how to teach! Ask them: 

- how many years they have taught 

- how many students do they teach a week 

- how long do students stay with them 

But be careful, because teachers with a lot of students may also not have enough time for you or not track your progress enough. 

An organized teacher who has many students is also a good choice. This means taking notes, keeping track of your progress and using some sort of register. 

Personal Note: At one point I had 60 weekly 1/2 hour private students. Though I was working long hours I had no problems keeping track of each student's progress and giving them my full attention during the lesson because I had a system. 

2) The level of current and past students is also something that is significant. If you are looking for beginner lessons look for a teacher who is skilled at teaching beginners. There are totally different teaching methods and styles involved in teaching different levels. 

3) Age range of students. It's best to divide students into children, teenagers and adults. Look for a teacher with experience teaching students of your age range. 

Training does make a difference 

Your prospective teacher should not only be trained at how to play their guitar. Ideally you want to pick a teacher who has also been taught by good teachers. Good teachers will always model their lessons on the good teachers' methods that taught them. These types of teachers will use methods and materials that worked well when they were learning and keep you away from methods that don't work. 

A teacher can also be taught by a school. College graduates are likely to have training only in classical guitar as most universities do not offer programs in popular music. But many instructors that I've hired have been to schools such as Musician's Institute in L.A., Grove School Without Walls, and Berklee College of Music in Boston, MA., which do offer popular music. 

The other way to learn to teach guitar is to take a course with the same name - though the only one I know of is the one I teach at the Starland Music Center using my proprietary system along with the principles and techniques of proper instruction. You can also get wonderful books on this topic (check out author Joe Livoti) and you can learn a lot from method books and testing the ideas on your students.