There are many, many voice teachers out there. How do you know which one is the best fit for you when you've never worked with any voice teacher before? If I could give you one precise answer to this, I'd be hailed as a guru in this business. Unfortunately, the answer is that it's mostly trial and error. BUT - there are some guidelines that can definitely help you in narrowing the field. First, if you can, get some recommendations from people you know who sing well. It doesn't mean their recommendation will be the right fit for you, but it's a good place to start.
When you contact a teacher ask about that person's training and experience as a teacher and/or performer. Does this person have experience in the genre of music that you are interested in? Has this person worked with beginners? with professionals? Are there any success stories to share about this person's students? Lots of experience working with various voice types usually expands a teacher's understanding of vocal production and how to get results from various "starting points."
When you get to the studio, do you connect with this teacher? Do you understand what he/she is trying to explain to you? Do you get any "Aha!" moments? Do you feel any vocal discomfort (a bad sign!). Do you sense that this teacher is capable of keeping your voice healthy as you progress? And, a simple one...do you like this person? These are practical points for assessing a teacher in the beginning. There's more, though...
DON"T keep going to someone just because your friend likes him or her. You're the one who has to develop your own relationship with your voice instructor. And, believe me, you've got to trust the person you share your vocal development with. You will be working closely with this person for a good period of time. You need to feel safe and confident that this person knows you well and sees beyond even what you can imagine for yourself. Does this person inspire you and help you stay on the path to your goals? Are you richer for the experience? These points give some definition to the difference between a really good voice teacher and a great one. You'll remember things a great voice has taught you all your life.
We'll continue with this topic. It's a good one - but these are some of the first questions for you to consider when you are looking for a voice teacher. Good luck!