If you're new to an area or to pet ownership, I would defenitly recomend shoping around for a vet. See if there is a local publication that has a yearly vote for the best of... contest that might include categories for pet care. Ask pet store staff who they take their pets to. Talk to other pet owners you meet and ask who they go to and what they think of them. If you find one that sounds promising, set up an apointment for an intro exam. Ask about the vets qualifications; where they got their degree, any additional certifications, vet association memberships, and do they specialise in any particular animal. Then watch how the interacts with your pet, what questions do they ask, are they willing to answer questions and do they explain things to your satisfaction, and are you comfortable talking with them.
I've been lucky. When I got my first cat, I just went to the vet down the street because they were close. The senior vet there was brusk and more of a dog person, but his new assistant vet and I hit it off well. I kept asking for her, and eventually he retired and she bought the practice. That started in 1980, and I've been going to the same vet ever since, even after I moved elsewhere in town. I now use a second vet hospital as well becuse they're closer, keep later hours, and take walk-in apointments. That's more convenient for my street rescues, but I'm not always sure of their competency on serious matters, so for that I go back to my original vet. I just lucked onto the perfect vet the first time.