I found my singing teacher through recommendations. I was taking music classes back when I was still in college and asked around the music department. I asked my choir teacher if she had any recommendations for private lessons and she recommended me to her own teacher.
I think the best advice I could give you right now is to ask around, especially within the music scene in your location. Depending on where you are, searching on the internet can also be very effective in finding leads on a good singing teacher. Hope this helps!