When I was preparing to move to Japan I did a lot of Japanese study. I had a year or so to prepare, but even after that much time my Japanese level was still low when I arrived. But, once you arrive and are immersed in the language, it becomes much easier to grasp.
"Japanese for Busy People" is a good system, and it is used by a few language schools in Tokyo. This site:
Japanese Language Free Study Material - MLC Japanese Language School is a good resource.
Before you move you should stock up on the basic things that you'll probably need. Start with clothes and shoes. Most of the clothing in Japan is either overpriced, or it is crap. You'll need at least 2 suits (dark navy or black) 4 or 5 dress shirts, and a couple pair of dress shoes. Rubber-soled dress shoes are best as they don't soak up water on the rainy days, and they are more comfortable when standing and walking.
Stock up on toothpaste and deodorant, the stuff they sell in Japan is so completely ineffective it is useless.
Remember that Japanese DVD players and such are region 2, so if you are coming from America you might find that your DVDs will not work in a Japanese machine. Most American electrical appliances will work in Japan if you remove the ground post from the plug.
Hopefully you have a drivers license in your home country. If you do, get it converted to a Japan license after you arrive. A driving test may or may not be required, depending on which country you are coming from, but either way, it's much easier to convert a foreign license to a Japan license than it is to go through the lengthy and expensive process you would have to go through to get a Japan license otherwise.
Make sure you have enough money to get buy when you arrive. If your company isn't going to supply an apartment for you, you'll need to rent one yourself. When renting an apartment in Tokyo, you'll need enough money to pay at least 3 months rent up-front. Some apartments will require up to 5 months rent in advance, which can be expensive.
Getting around Tokyo is very easy, though you will probably be overwhelmed the first few days you are here, but hopefully someone from your company will spend a day or two with you to show you how to get around.
If you are coming in 2 months, your new company should have already started the visa sponsorship process. They should have requested that you send them your passport and the necessary paperwork, and shortly before you leave your passport will be returned with your certificate of eligibility for your work visa. You will have to send/take your passport and COE to a Japanese consulate before you you leave (it'll take 2 or 3 days), where the permit will be affixed to your passport. You will get the actual visa when you arrive in Japan.
The first thing you need to do when you arrive is get a hanko (name stamp). You'll need need this to do things like open a bank account, get a license, rent an apartment, etc. A hanko shop can be found in most neighborhoods, and they are inexpensive. Someone from your company will have to accompany you to a bank (probably Japan Postal Bank) to open an account so you can get paid each month, there is no such thing as checks in Japan.
I'm sure others will have other advice.