How did your family choose a doctor when we were growing up? A friend, a referral from a friend, the doctor all your friends went to? Life was so simple. Now it's about insurance coverage, hospital affiliation, specialty certifications, yada, yada, yada.
I'll also throw in the importance of having a primary care provider who is willing and able to act as your care coordinator if you have a serious diagnosis that requires the involvement of one or more other providers.
I'm proud to be a contributor to this great article in St. George's University Medical School blog on how to go about finding a provider whose skills, availability--and let's face it--style of practicing medicine is a good fit with you: HOW TO CHOOSE A DOCTOR