A Japanese contact
Studying in Japan as an exchange student on graduate level requires a guarantor/contact person in Japan who will assume academic responsibility for your stay. Make good use of the staff at NTNU. In order to arrange visa and a contact person, it is important to find someone with good personal connections to your academic environment at home. This is one of the first things you should do. As you will become quite dependent on your contact person, it is an advantage to know a bit about his/her personal behaviour.
Financial support
You should then arrange the financial support for your stay. See the Norwegian State Educational Loan Fund (NSELF) for updated information for studying abroad: http://www.lanekassen.no/templates/SectionPage____5332.aspx (English).
Ph.D students will not receive financial support, as these students usually have another source of funding, but there are other possibilities support in these cases.
In addition to NSELF there are other scholarships one can apply for, both in Norway and Japan.
Housing and cost of living
Housing in Japan will not be the same as in Norway. A student will often have to settle for 10m², at a somewhat higher price. Cost of living in general is higher than Norway.
Talking to people with some personal experience from studying or working in Japan is smart. This can help you avoid many of the more common pitfalls. Japan has a different custom and behaviour than you are used to, so some good advise will help you a long way.
Links
See the overview of “Scholarships & Funds” on the homepage of Japans Norwegian Embassy:
http://www.no.emb-japan.go.jp/