I learned a bit of Japanese (up to level 2 on the Proficiency Test) over the three years. There are plenty of ways to study when you get to Japan - the JET programme runs an official language course from October to about May, and you can find Japanese teachers or people prepared to do language exchange easily. The job also usually gives you a lot of free time during the working day that you can use to study.
As for what you could achieve over one year - it varies a lot depending on your own aptitude for learning languages, and your interest! If you can maintain the enthusiasm... learning from scratch, after one year I would say you could have a good basic level of Japanese that would get you through most everyday situations (asking the way, small talk and introductions, ordering in restaurants etc). As far as reading goes you could expect to know the first few hundred basic characters, as well as hiragana and katakana. Some people probably learn more than this in a year, and a lot of people learn much less... It's possible to have fun in Japan and get by without ever trying to learn the language, like British expats in most of the world do!