If your region supports it, you can simply sign up for the program from the phone settings. From there, go to Exposure Notifications and then select your appropriate state. The framework uses Bluetooth Low Energy to exchange a private key with all nearby phones using the same software. If you come into contact with someone who has tested positive for COVID-19 (that person will have to report this to the app by stating it as such), the phone will notify you that you may have been exposed.
In order for the exposure notification system to be operational, the public health authorities in your region must accept it. So far the list of US states and regions who support it include Alabama, Arizona, California, Colorado, Connecticut, Delaware, Maryland, Michigan, Minnesota, Nevada, New Jersey, New York State, North Carolina, North Dakota, Pennsylvania, Virginia, Washington, Wyoming and Washington, DC.