You can look in the yellow pages, close your eyes and pick at random.
You can wait until you see a flyer, lettered vehicle or mailer.
Plenty of good painting contractors use these methods. Some work mostly by word of mouth and these painters can be harder to find. If you are looking for a painter (or a plumber, electrician or roofer, etc.) there are several options.
Call the local Homebuilders Association for your town, in Cedar City, see the BIA.
Call your local paint supply store, not the big box stores, but a store that sells nothing but quality paint, like Sherwin Williams or Jones Paint and Glass, your town may have others. Ask the manager at the paint store who he can recommend.
Friends and neighbors can know a good painter, ask around.
The internet can help you too! Google "painters in my city" and look at their websites.
When you do search, you will find many companies like Service Magic or Reliable Remodeler. These are "Lead Service Generator Services". There is a lot of controversy concerning these companies. They work by charging contractors a set price for each lead. You are the lead! When you submit your name and project, they send your information to the contractors who have paid. Sometimes they sell your name to many contractors! They have no control over quality of contractor. Look for a local painter that has local references!