Due to the US system of government, public health laws are largely enforced at the state and local level. The federal government does not (currently) play a role in quarantine restrictions for incoming travelers. The Centers for Disease Control recommends that higher-risk travelers self-isolate as much as possible upon arriving in the US. However, this recommendation does not have the force of law.
Instead, there are 50+ sets of laws that need to be checked (there may in some circumstances be local laws in place in addition to state laws.) The AARP does seem to be maintaining a long list of COVID-related restrictions for all 50 states & DC. It includes descriptions of quarantines for arriving passengers, along with other things such as re-opening phases, restrictions on public gatherings, etc.
In the interests of keeping this answer manageable, I'll provide a couple of examples:
North Carolina does not currently impose any quarantine restrictions on incoming travelers. They simply state that
Domestic and international travelers to and from North Carolina are urged to follow guidance from the U.S. Centers for Disease Control and Prevention as well as the U.S. Department of State and their airline or other travel company.
New York, Connecticut, and New Jersey have entered into an interstate agreement to require any travelers arriving from highly affected states to self-quarantine, and to issue fines to travelers who do not self-quarantine. I will discuss the situation in Connecticut below, since it is my home state and the one I am most familiar with; however, the rules for New York State appear to be largely similar.
[A]nyone traveling into Connecticut from a state with a positive test rate higher than 10 per 100,000 residents, or higher than a 10% test positivity rate over a 7-day rolling average, are directed to self-quarantine for a 14-day period from the time of last contact within the identified state. This list will continue to be updated on a weekly basis on Tuesdays as the situation develops across the country.
"Affected travelers" arriving in Connecticut are required to fill out a form giving their name and whether they are exempt from self-quarantine. Affected travelers are basically anyone who has spent more than 24 hours out of the last 14 days in a higher-rate state, and who will be spending more than 24 hours in Connecticut. In particular, anyone who is simply traveling through Connecticut on their way to another state, via road, air, or rail, does not need to self-quarantine. New York applies a similar rule to travelers transiting through New York, including those connecting through New York City airports (JFK, EWR, or LGA); from the link to the New York rules above:
The requirements of the travel advisory do not apply to any individual passing through designated states for a limited duration (i.e., less than 24 hours) through the course of travel.
Failure to self-quarantine, or providing a misleading form, are subject to civil penalties of $1000 in Connecticut ($2000 in New York.) As of last week, a total of seven people had been fined by the state of Connecticut under this order. There does not appear to be publicly available information on precisely how the authorities became aware of these violations—which is perhaps understandable. However, there are publicly open channels for the public to report suspected violations of this quarantine order, which may have something to do with it:
If I know someone has traveled to Connecticut from an affected state and is in violation of the self-quarantine rule, is there a channel for reporting this? Anyone wanting to report any violations of the self-quarantine order can either call 2-1-1 or email email@example.com.