Upvote:3
According to the DHS announcement and fact sheet, the procedures for people who have been to Schengen Area countries within the last 14 days who are exempt from the ban (US citizens, permanent residents, and their immediate family members) are the same as the procedure for people who have been to Mainland China (but haven't been to Hubei province) or Iran within the last 14 days.
Basically, they will have to arrive in the US at one of 13 designated airports, where they will undergo medical examination. If they have no symptoms, they will be asked to self-monitor their health and limit interactions (the government also calls this "self-quarantine") until 14 days after they have left the Schengen Area, but there are no formal restrictions on where they can go.
Only people who have been to Hubei province within the last 14 days are subject to a formal, mandatory quarantine so far.