There are many accommodation choices in Japan, but few are cheap. If you plan on camping you can find campsites from free to up to Y4000 yen, however most are around Y500. Next up the ladder is a youth hostel with an average cost of Y2500. Japan is not a backpacker's country, so backpackers and youth hostels are not abundant as other places, but you should be able to locate one in most areas.
Some temples offer lodging for travelers, and they can be another cheap option.
If you do have a few yen to spend, you give yourself a lot more choices. Youth Hostels Budget travelers will definitely want to stay in youth hostels. They are comfortable and inexpensive, and are a good place to get information and meet people. However, it's a good idea to check what time the close, as some can be run very strictly. If you wish, you can literally plan your trip around where they are located.