If you are from a country without visa exemption, you will have to secure a visa through your local travel agency or the nearest embassy in your locale, of which address may be found in this link.

The Ministry of Justice have rolled out specific regulations about visas issued for the purpose of internship. Said regulations may be found in this link. The regulations will allow you to qualify yourself, if you are eligible for an internship in Japan. Should your  personal assessment reveal that you are eligible, you may already coordinate with a host company about it and prepare the following general documentations needed for a Japanese Visa:

• A company invitation letter, specifying details of your visit for the purpose of internship 
• A passport valid up to 6 months after the date of the Visa’s expiration and at least two blank pages for the visa
• Passport-size photos with the following specifications:

1. Dimensions: 4.5cm x 4.5cm
2. White background
3. Taken in the last six months
4. Head should be staring straight ahead, with a neutral facial expression
5. Entire face has to be visible
6. Name and birthdate have to be written at the back

Additional requirements may depend on the company you will be landing in and also on the list of requirements from your university.