How to know what's important to consider when hiring a singing teacher
Having worked as a singing teacher and having also been in receipt of many singing lessons myself, the most important thing to consider is why you are having the lessons in the first place. This in itself should help you find the right teacher for you.
For example, if you are looking for someone to help you with an audition, then really you are looking for either a) an accompanist or b) an actor or actress who knows the business, but who can also play piano. These teachers tend to me much cheaper than a tutor who is perhaps teaching at a top drama school and who is really going to help you with technique.
So, if you are looking for someone to assist with technique, or to help you get into a drama school, then I think finding someone who is older and who is currently working within and educational establishment, is probably the best idea. It means that they will know what the business is looking for at the moment and this may even help you when applying for schools.
One main thing to consider, is what the teacher advertises as their own experience and/or training. If you want to develop opera skills, then find a teacher who trained classically. Do not confuse Musical Theatre or Pop with Classical or Opera techniques - they are simply not the same.
The last and most important thing to consider is cost. I have had singing lessons in the past which have ranged from £15 an hour to £70 an hour and never again would I pay beyond £40. The reason for this, is there are plenty of teachers out there with a wealth of experience who are charging up to £40 and they will all tell you that the reason they don't charge beyond that, is because NO one hour singing class is worth it. No matter who is teaching.
My current singing teacher is the head of singing at a top drama school and if anyone deserves to charge £70 or even £100 an hour, it is he. But he doesn't. For that, I feel credibility is far higher and I think this should always be a major deciding point in securing a new singing teacher.