Well you could always visit ACT
Back to the topic. Google will be your best friend. Majority of PCB shops have a website, and so you'll be able to locate them. Here's some ways our customers have found us on Google. They search some of the following ways:
Keyword + Qualification
Printed Circuit Board, Rigid Flex, PCB, PWB, PCBA, etc...
: ISO, IPC, Milspec, UL, etc...
PCB ISO IPC Certification
Certifications are usually a good sign of quality. Also look out for good service, on-site design/engineering team. If you really want to get in depth, go look at their BBB record. Plus see if they will include Traceability codes on their boards, if you request sample boards it might help, but be wary usually they'll send out their better boards.
Although most people on this forum will be looking to do smaller orders, so the best is to do a collective order with a company. Gather a group of people, either your friends or people from this forum, and place an order together. This will give you better pricing.