If it is minor ailment you can head straight to a drugstore and they will advise you. For anything worrying / serious head to your nearest hospital. There aren’t many local clinics available so most people use the hospital. Health care is usually very cheap however do hang on to your receipts and bills for you insurance.
Chinese hospitals tend to be cheaper but are much harder to navigate if you don’t have a good grasp of the language. There are many International hospitals that are equipped to take patients from all over the world.