If you are staying in Japan for a year or more you may want to rent.
Unfortunately, foreigners in Japan have a reputation for leaving houses and apartments in bad condition and for leaving with unpaid bills.
As a result of this it can be difficult to find somewhere to rent in Japan.
It is possible, however, but you can expect to pay at least 4 weeks rent as bond (refundable if you look after the place) and a further approximately 4 weeks rent as "key money" (non-refundable).
They MAY also want a Japanese person to act as garantor for you.
If you have any more questions about renting in Japan you will find links to foreigner friendly real estate agents on this page or you can post questions here...

If you are looking in the Tokyo area, I highly recommend transborders. They are like a japanese agent but they work mostly with foreigners (in english too). They can get you a typical japanese apartment (as opposed to the small, way overpriced foreign targeting rooms) and they confirm with the landlord that foreigners are okay BEFORE showing the floorplans. http://www.transborders.co.jp/realestate/index.php?language=2

Sounds good!
Do they need references?
Key money and bond?

They are an agent, they don't own their apartments so the rental policy and fees etc vary depending on the landlord.

Oh well, at least checking if gaijin are accepted first is a good idea!

yeah, I got my current apartment threw them, it was relatively pain free. Still expensive though but nothing you can do about that.