There are two main types of Japanese Health Insurance: National Health Insurance and Employees' Health Insurance
Once you have joined the health insurance system, you will be issued with an insurance card ("hokensho"), which you must bring with you every time you pay a visit to a clinic or hospital or other medical facility. If you forget your card, you may have to pay the full amount for treatment, though this is refunded later.
All residents of Japan who are planning to stay in the country for at least one year and haven't joined another health insurance program are entitled, and expected, to join the National Health Insurance Program.