I don't know how much help I can be, but I'll try.
First off, how is your Japanese? Can you speak and read? If so, any information that I can give you will be much more useful, as I've never tried to find an apartment through the medium of English in Japan.
Secondly, will you be working wihile in Japan? If so, doing what? If you plan on teaching English while here, oftentimes your employer will provide housing for you, so you won't need to search on your own.
Some basics on apartments in Japan.
They are smaller than apartments in America.
Although this is changing somewhat, it is customary to have something called "reikin" and "shikikin" when signing the contract. "Reikin" is non-refundable and is basically your saying thank you to your new landlord for letting you live in his her property. It generally runs about 50,000 yen. "Shikikin" is like the deposit you pay for an apartment in America with a couple of notable exceptions:
1) It does not accrue interest.
2) You probably won't get much back anyway.
"Shikikin" is sometimes referred to as "hoshokin". (There might be a difference between the two, but I'm not 100% sure what that difference might be.)
Contracts generally run for two years.
Generally speaking, a guarantor (co-signer) is needed, although it is possible to find apartments that do not require them. Being a foreigner might make it difficult to find one that will accept you, however.
There is something called "shokakukin" that you should look out for. If the apartment has this, it means that you will have to pay this amount to the landlord, usually upon leaving the apartment. "Shokakukin" basically means "depreciation money". Not all apartments have this, so try to avoid it if possible.
Apartments are described by the following scheme.
2LDK
Here "2" refers to the number of generic rooms.
"L" refers to the presence of a living room.
"D" refers to the presence of a dining room.
"K" refers to the presence of a kitchen.
The absence of one of thise letters usually means that that particular room is not part of the property.
Unless otherwise stated, apartments are unfurnished. This means that there is no refrigerator, no lights, no cooking range, no curtains, no anything.
I can't speak for the situation in Tokyo specifically, but around these parts, I would make sure that I had about 300,000 yen on hand in cash for signing the apartment lease.
I'll try to add anymore information later if I can think of any.