An internship in Japan requires you to have a general visa. You can apply for this visa at the Japanese embassy. If you happen to receive an internship allowance then there will be different rules. Once you arrive in Japan, you are required to report yourself. This also goes for your health insurance.
An internship in Japan requires you to have a general visa, which is valid for one or two years. The visa is free. A general visa needs to be requested personally at the Japanese embassy. First visit the website of the embassy to download the application form. Fill out this form and bring it with you, along with your passport, passport photograph and possibly your Certificate of Eligibility. The application process takes around a month, so make sure to visit the embassy on time!
The application process is shorter if you specifically are invited by a higher education institution. In these cases, the institution will request a Certificate of Eligibility for you at a regional immigration office in Japan. Ask you internship company about this. Make sure to have all the required documents. You are required to prove that you have enough livelihoods to pay for you stay abroad. The entire procedure should only take a few days with a Certificate of Eligibility
If you have a different visa than a tourist visa, then you are required to report yourself within 90 days to the local immigration office. They will then take your fingerprint and you will be given the Alien Registration Certificate. This is a card that you are required to carry with you at all times.
In Japan it is uncommon to receive an internship allowance. If you do happen to receive compensation then you will have to deal with different rules and/or residence status. Contact the Japanese embassy in the Netherlands if this is the case.
With an Alien Registration Certificate you can join the Japanese National Health Insurance. This is relatively cheap for students. How much it will cost you exactly differs from city to city. With you proof of enrollment you will be treated at all healthcare institutions if necessary.
The Japanese health insurance covers 70 per cent of all medical costs, including dental care. The remaining costs can be declared through your Dutch insurance. Just make sure to take supplementary insurance while you are still in the Netherlands. Also ask your internship company if you are insured at the company premises if a work related accident would occur.