Landing Permission

Is it likely that someone would be declined landing permission? I am moving to Korea, and want to travel round Japan for a month before I go there from Australia.
I read that if you have a ticket in and out of Japan you will have landing permission, but also that you have to provide bank statements and other information. What should I bring with me?

First you have to check: Will your nationality as per your passport need an entry visa for Japan. http://www.mofa.go.jp/j_info/visit/visa/02.html
Then all passengers have to fill in an entry form on board of the incoming airplane. Passport with or without visa and the entry form will being checked by the immigration officer. It may happen he will ask you about return flight and financial funds.

We need to know your nationality to answer this question. If you are from a country with a visa waiver agreement with Japan (most Western countries and many others) then all you need is your passport.

I'm travelling on a NZ passport.

You have an NZ passport which is visa waiver with Japan, I don't see any reason why you would be denied entry, unless your motives on entering Japan are not what as it seems. But for tourism, and if you've never been deported from Japan before, I don't see any problems.

then visiting Japan is like visiting Australia or Fiji. Your passport is stamped with a tourist permit when you arrive, you can stay 90 days. It's no more complicated than that.