Your dentist should be thought of as your partner in looking after your teeth, gums, and mouth as you should be seeing them on a regular basis over the years to come.
You should approach finding a dentist as a long-term proposition. Seeing the same dentist over a long period of time provides you with "continuity of care" where your dentist knows your history of dental treatment which cannot be matched by regularly changing dentists.
One great way to begin your search is the ADA's Find-a-Dentist search engine which locates ADA member dentists near you. Word of mouth is also a great tool. Ask your friends and family that are happy with their dental practitioner for a recommendation. If you are moving towns, ask your existing dentist if there is a dentist they can recommend in your new location.
Everybody has the right to choose their own dentist. This choice should not be compromised by private health insurers who seek to convince their customers to use their contracted or 'preferred provider' dentists.