If you are making a local or intercity call, you need to use an NTT phone. KDD handles all foreign calls. All public phones are clearly marked with each company's sticker. Gray phones, which have screens with instructions in both English and Japanese, accept phone cards only. As a general rule, phones that accept phone cards will allow you to make international calls.
Telephone cards are available at grocery and convenience stores, as well as kiosks.
Note that special souvenir phone cards can cost more for the same number of minutes. You may want to purchase or rent a phone and set up an account in Japan. NTT DoCoMo, Japan's largest cell-phone provider, has two main plans to suit your needs. The Digital Plan works throughout the entire country, in cities and suburbs. The City Phone plan works primarily in major cities.