There are really two things to consider in finding a plumber: actually finding one, and finding one you'll be glad you found. It is a two-pronged approach that leads to plumbing satisfaction. And, as we need plumbing as long as we're around, it needs to be a satisfactory and lasting relationship.
You can find a plumber in several ways. There is the rather old-fashioned dead tree approach, where you use that book with the yellow pages and find an ad that appeals to you. Then you employ one of those retro things, I believe they are still called phones, and call the company you have chosen to establish verbal communication. That works, after a fashion. You can tell if they are pretty serious about their business, by the ad, and you can tell a lot by talking to them, being a wise and careful shopper as you are.
Another way is the even older-fashioned way, called talking to people. Some good people to talk to would be the neighbors, friends, and people you meet in the community, like at church, PTA, or even the bowling alley. Those folks will know about local plumbing contractors, and hopefully they will be willing to share their special local knowledge. You want to watch out for special interests, of course. I mean, if the company they are recommending is owned or run by themselves or their near and dear relative, you might want to seek a second opinion on that.
Yet another way is the most modern to date, and that is the computer or something much like one. Plumbing companies have web sites now, just like all other kinds of business. Like other kinds of business, there are good and bad plumbing company websites. The best will give you some real information, including licensing and experience qualifications, along with some testimonials and perhaps some inspiring pictures. The web site will also have a useful list of phone numbers, email addresses, and other contact information. A web page has a lot more room than a phone book ad, so much more can be offered.
Each of these has it's problems as well as advantages. The phone book has a lot of condensed information in a small space. The ask about method may get pretty chatty, and depends on the reliability of the source, but can get you in contact with reality quickly. The web page is of course impersonal, and needs to be verified by contact or research.
Probably a combination of at least two of these methods works best to reach a successful conclusion. You want to find a plumber that can do what you want done. You want to find a plumber that will not over charge you, or cheat you in any way. You want to find a plumber that will do the work well, neatly, and quickly. So look around, either on paper or on the web, ask around wherever works for you, and use your own good judgment and the wisdom gained from experience. Good reliable plumbing contractors are available, and you know how to find them.