I know it can be overwhelming finding your voice teacher. First, you have to actually find possible teachers, then you have to consider your budget, your schedule, their schedule and your goals as a singer. And really, how can you know which of the teachers you found is going to be your best option?
At this point I find that a lot of students just want to know what vocal "style" the teacher teaches and he or she uses that as the determining factor. I'd like to propose a different approach to evaluating your teacher possibilities:
First, I am convinced that all singers will benefit from having a teacher with a classical education. You may not want to be an opera singer, but the techniques that a classical teacher can help you acquire will benefit any vocal style. They'll help you to avoid injury, increase your vocal and a plethora of other skills. A good teacher will adapt his or her teaching methods to help you with multiple styles of music. Usually if I have a student who is interested in singing pop or country or any other popular style, we'll alternate repertoire pieces between classical songs that I've chosen and songs of their choosing (although this depends on the skill level of the singer and how much classical technique I think he or she needs first). So, find a teacher who is classically trained. Read the teacher's resume or send them a message asking about his or her training.
But if you're not trying to match the singing style of the teacher up with your own, then how else should you evaluate the teacher?
Evaluate the teacher by their teaching style. This will probably require you to set up a few trial lessons, but it's worth it. Finding your teacher is a lot like finding your perfect hairstylist or significant other; you may need to date around. You may find a voice teacher who is just perfect for you, even though others may not like him/her. Or you may find a voice teacher who is just like that perfect hair stylist that everyone loves because they're just able to communicate with everyone.
What makes a good teacher good? In my opinion, it's the ability to explain a concept many different ways. One of the things that I think makes me a good teacher is that I was probably a very frustrating student to work with. I needed singing techniques explained to me over and over in different ways before I actually accomplished anything. Often I would practice for weeks and seem to make no improvement--I might even regress! But once I got a concept I GOT it, and now I have an arsenal of ways to explain singing techniques (because I had to have it explained to me so many different ways!).
I always watch my students closely for body language that tells me they're not understanding what I'm explaining and try different tactics. But don't depend on your teacher to read your reactions! When you're in a voice lesson ask your teacher to explain things differently. Tell your teacher you don't understand, or tell your teacher what you think they meant and ask him or her to correct you. If your teacher can't, he or she may not be the right fit for you. It's nothing personal--"it's me not you," you know? I've had teachers who were such wonderfully gifted singers naturally that they were just not that great at explaining things, and as a student I really needed explanations. I needed technical explanations, I needed lots of imagery, and I needed to be able to mimic the teacher. Look for that right fit and don't be afraid to keep looking for another teacher if the one you're studying with currently isn't working out.
When you do find that perfect teacher you'll be excited to go to your lessons because you'll be making progress and achieving your goals as a singer. So go find that teacher!