Korea's Central Accident Investigation Headquarters and Central Discharge Countermeasures Headquarters have opened its official English website on COVID-19 measures and report for foreigners. You can find the latest information on COVID-19, ranging from case report updates to changes in policies. 

http://ncov.mohw.go.kr/en/ (English)  

http://ncov.mohw.go.kr/cn/ (Chinese) 

Important excerpts include:

Preventing inflow at the immigration bureau

Immigration procedure after visiting non-quarantined regions

All entrants are screened for fevers using heat-sensing cameras upon entry at the Arrivals Hall, and anyone showing symptoms, including fevers must fill out a physical condition survey.

Immigration procedure after visiting quarantined regions

Anyone who has visited (sojourn or layover) a quarantined region during the observation period must fill out a physical condition survey and submit it to a quarantine officer when entering the country. In accordance with Articles 12 and 39 of the Quarantine Act, violations are punishable by a maximum one year prison sentence or a KRW 10 million fine

Special immigration Procedure (as of March 19, 2020)

The Korean government has enforced an entry ban on foreigners arriving from Hubei Province, strengthened visa screening, and tightened quarantine inspections of entrants from China (including Hong Kong, Macau), Italy, and Iran.

In particular, the Korean government began applying special immigration procedures to all passengers entering Korea from Hong Kong and Macau (February 12), Japan (March 9), Italy/Iran (March 12), five major European countries (France, Germany, Spain, U.K., Netherlands, March 15), the entire European continent (March 16), and has since expanded its scope to include all passengers (March 19).

Furthermore, all domestic residents and foreigners entering Korea will be subject to temperature checks during special immigration procedures and required to submit a Health Declaration Form and Travel Record Declaration.

Special immigration procedures for passengers entering the country from China (including Hong Kong and Macau), Japan, Iran, and Europe entail a temperature check, physical condition survey (based on self-declaration of symptoms for entrants from Japan), checking whether they have visited Hubei province, and verifying their address and contact information within Korea before allowing entry. Passengers who have travelled to Hubei province within the past 14 days or are unable to provide a number at which they can be contacted within Korea may be prohibited from entering the country. Moreover, a list of all entrants will be provided to cities/provinces to assist local governments’ observation efforts.

Entrants subject to special immigration procedures must provide their contact information and address within Korea, and install the Mobile Self-diagnosis Application so that their temperature and other indications of possible infection may be monitored. After installing the Mobile Self-diagnosis Application on their phones, entrants subject to special immigration procedures must check their symptoms on a daily basis for 14 days beginning on the day after entry and enter whether they are showing symptom on the application.
※ Self-diagnosis items: fever (37.5℃ and above) or feverish symptoms, coughing, sore throat/throat pain, difficulty breathing/shortness of breath

If you are showing signs of even one of the symptoms you must place a call to the call center (☎ 1339) and follow the directions. If you fail to comply with the app installation and self-diagnosis recording requirements, you may receive a phone call from the call center and additional measures may be taken to locate you if you are unreachable.

※ Support is provided onsite so that travelers may install the self-diagnosis app before departure or while waiting during special immigration procedures.

Providing health care organizations with overseas travel histories

The South Korean government provides information to healthcare facilities using the system that checks for qualifications of examinees, the International Traveler Information System (ITS), and Drug Utilization Review (DUR) so that medical staff are allowed access to people’s overseas travel history.