Ask your current singing teacher, choir teacher, or person in charge of music at your school (if you go to one) for advice on some private teachers. Usually someone who is already teaching singing in some capacity will have a good idea of singing teachers that you can use. He sometimes has a list of teachers available, and he might even teach lessons himself.
Check with music stores, or stores that sell musical equipment in your town or general area. Typically, singing teachers who have private lessons let these stores know who they are, so that the stores can recommend them.
Look in your local paper for anyone advertising singing lessons.
Check community notice boards, any community online sites, and talk to friends or community members who might know of someone who is teaching lessons.
Contact your local university or college, even if you don't go there. Talk to someone in the music department. She will be able to give you several suggestions for a private teacher.