Moving

Obviously anyone coming to Japan will need a place to stay. Most conversation school teachers and students have apartments prepared for them by their schools. Some Japanese language schools can set up apartments for students as well. Finding an apartment in Tokyo near the workplace/school is sometimes difficult. (Average commute for office workers is an hour by train.) The farther out you go the more likely you are to find an affordable apartment but "affordable" is a relative term, of course. Average apartment rent varies quite a bit depending on size and location. Those who are used to New York or Hong Kong rents will not find any surprises here.
Japanese room size is defined by how many tatami mats will be used to cover the floor. The most common size is a 6 mat room. 4.5 mats is about the smallest reasonable space for living. Apartments will be described similar to "6, 6, 4.5" which would be a place with two 6 mat rooms and one 4.5 mat room.
In apartment ads "L" refers to "Living room" a room off the kitchen. "D" is "Dining", which means that the kitchen is large enough to fit a table into. "K" is "Kitchen" and means that the apartment has a kitchen. So "3LDK" means 3 rooms, a living room space and a kitchen with dining area. A 2DK reasonably near a train station on a major line will cost about 100,000 yen a month. The grossest apartment I have even seen (much less lived in) was a single 6 mat room on top of a tofu factory in a pre-war building. Rent was 18,000 yen - miraculously low. (Just the other day, we were marvelling at somebody's two 6 mat + kitchen 10 minutes walk from a major station with 72,000 yen rent.)

When first renting an apartment the renter needs to pay key money (reikin) which is basically a bribe to the landlord to let you live there and security deposit (shikikin). These are usually in amounts of one or more months worth of rent. So if you find an apartment for 80,000 yen and it has a "2,1" policy you have to pay 160,000 yen (2 months rent) worth of key money and 80,000 yen for deposit.
If a realtor helps you find the apartment the normal payment is one month of the apartment's rent for services.
The first month's rent is also usually paid in advance. The 80,000 yen apartment in the example above would thus require:

Or about $4,000 just to move in and live that first month.
You can get most of the deposit back in most cases (unless you really trash the place) but key money is non-refundable. Apartment contracts are commonly 2 years long and renewal normally requires another key money payment. Sometimes this is lessened or even waived if you have lived in a place for long enough. It is also usual to raise the rent a few thousand yen when making the new contract.

 Greg Tavares has a great page about apartments in Japan.which I strongly suggest reading. There are also many other items of interest in his site so read the whole thing.