Look for the "Uketsuke", Hospital Care in Japan
Injured in Japan? Read this Article about Hospitals in Japan
Although my experience at hospitals in other countries is limited, I don't think the process at a Japanese hospital is particularly unique. All you have to do when you get to a hospital is to find the "uketsuke" (front desk), which is usually located right by the entrance, and talk to a nurse about your health concerns. The nurse will determine the type of help you need and ask you to wait in the front lobby. Here, you are often given a paper with a number on it. When preparations are complete, your number, or name, will be called and you will be taken to a doctor where you will receive help.
Like in any other country, though, it is always best to make an appointment beforehand. Hospitals can get busy, especially on weekends, and you don't want to wait a long time in the lobby.
Also, if you cannot speak Japanese, you may want to avoid smaller hospitals since they are unlikely to have English support. You can look for English-friendly hospitals online or you can visit one of the larger ones that usually have doctors who have studied abroad or other people who can speak English.
I hope you don't have to seek help at a hospital during your stay!