How do these people know they have Coronavirus

There are private labs that have developed their own test kits. Those labs have more of their own test kits than government agencies have of the official CDC test kits.

There is a lab in Birmingham that has developed its own, FDA approved test kit. They are doing drive thru testing (doctor order or physician on site recommendation required). This lab has said they can do 10,000 tests per week. Results are available in four hours.