Public transport

Public transport: Train, Bus etc.
Train and bus are used widely in Japan. There are bullet train, express train, local train, subway etc. You can check the details at the JR website (divided into JR east, JR west etc). There are private company running the railway too.

Japan Rail Pass http://www.japanrailpass.net/
JR East http://www.jreast.co.jp/e/index.html
JR West http://www.westjr.co.jp/english/global.html
Tokyo Metro http://www.tokyometro.jp/en/index.html

Osaka public transport information http://www.kotsu.city.osaka.jp/foreign/english/index.html

Anyway, if you are traveling a lot using train e.g in Tokyo area, check out the 1-day pass ticket. Cheaper but valid only for certain distance and depends on the railway company.
I remember taking JR train using the 1-day pass ticket from Yokohama to Tokyo, and then make a stop at Tokyo St., Akihabara St., Ueno St., Shinjyuku St., Shibuya St., Harajyuku St., Shinagawa St and lots more. It costs around 1350yen. Usually, one short ride will cost around 150yen and above.
Bus and subway also have the 1-day pass ticket. For example, subway in Osaka, 1-day pass costs around 800yen during weekdays and 600yen during weekends and public holidays.

JR train

City Bus

If you like to travel using train e,g travel from Tokyo to Kyusyu, I suggest you to buy seishun 18 kippu. You get 5 tickets, price around 12000yen. 1 ticket can be used per day. You can travel as far as you like using the ticket.

If you are a visitor, you can buy unlimited-shinkansen-ride ticket and can ride the shinkansen all over Japan for a certain period of time. Price is below 30,000yen per person.

Bullet train@shinkansen

You can check the train time table by buying the time table book or check below websites.
http://transit.loco.yahoo.co.jp/ (time table in Japanese)
http://www.hyperdia.com/ (time table in English)
http://www.jorudan.co.jp/english/　(time table in English)　

Tokyo JR train map

Tokyo Subway train map

Osaka Subway train map