Koreans generally do not take time off from work for being ill. However, exceptions can be made for foreigners, and contracts often include 3 days annual sick leave. It is important to recognize that these are not extra days to be taken off. If you call in sick you will often be visited by your employer who, in their concern and empathy, will drive you to the hospital (not a pleasant place to be). If you are not at your residence or if you stink of the previous night's events they are not going to be pleased.
Since your co-workers are automatically the often-unwilling recipients of your classes if you call in sick, it's not a good idea to do so unless you really are sick. Hangovers, or just having a bad day, won't be acceptable excuses for missing teaching to either coworkers or management.
Legally, for any sick day taken, your employer can deduct a day's salary unless you present an official note from a doctor. In practice, most employers don't ask for this note unless someone has been absent for more than one day or has a history of one-day illnesses.
