If you are thinking of traveling around widely in Japan using public transportation, there are some tips to save money.
Japan Rail Pass (or JR Pass) is well-known. It is useful if you travel around Japan using JR lines, including Shinkansen bullet trains.
If you are thinking of going to Hokkaido or Okinawa or anywhere far away from your starting point, some air fares exclusive for foreign tourists would be cost effective options.
You can also find some cheap seats in LCC airlines in Japan.
I hope this helps.