In general, (at least in AZ) an N.D. can do anything an M.D. can do plus more. By this I mean they can prescribe drugs. But that isn't their goal. Their goal is to help you activate your body's own healing ability. This can be through nutrition counseling, lifestyle counseling, supplements, homeopathy, acupuncture or physical manipulation. I'm sure there's other modalities that I'm forgetting.
Like other physicians, they usually specialize in one area or another. And how they charge varies.
We found ours through a friend. She has a women and children practice and I use her mostly as a pediatrician. (She used to include midwifery in her practice, but now refers that out because she didn't like the hours!) We see her for all my daughter's well-baby visits and I call her in the middle of the night for advice if my baby gets that sick. She supports my decision not to vax and supports extended nursing. I pay her out-of-pocket for each visit. I could try to sumbit these to my insurance for reimbursement, but I haven't.
I think the best way to find a good one is to just ask around your area. Then schedule a consultation and see how you feel about him or her and decide if their scope of practice includes what you need. If you have a naturopathic clinic in your area, you could start there. This would give you access to many drs with different specialties.
I love having an N.D. Good luck in finding one if that's what you decide would be best for you!