The main basic telephone service in Japan is provided by NTT (Nippon Telephone and Telegraph Corporation), which used to be a public monopoly. Here are some useful numbers for contacting NTT. When selecting a telephone service, make sure that it is compatible with whatever internet service you wish to use.
KDDI, SoftBank Telecom, and other companies have a wide range of money-saving services that can be used from NTT phones. For example, when you dial from a normal NTT phone to a mobile phone, you can use SoftBank Telecom and save money by using the 0088 prefix.