First, are you Canadian, Australian, British, or Kiwi? If so, then you can count your lucky stars, because being from any of the above qualifies you for a working holiday visa which lasts for 6 months but can usually be extended for up to a year, meaning you can work legally in Japan for that period of time, with no need for qualifications of any sort. BUT, you must have a certain amount of cash in the bank first (usually $2000/£1500) to show, you must be under 30, you need to have good health and no criminal record, and you can only apply for it once. Another big hitch is that you can't work in places which are regulated by the Law on Control and Improvement of Amusement and Entertainment Business, such as clubs and pubs. But just because you're not supposed to do it, doesn't mean it's not possible, that's all I'm saying. Probably the scariest news about getting working holiday visas is that they're limited in number, and especially now with the football going on in Japan/Korea, you can expect quite a few Brits are probably hoping to work their way through the whole tournament in Japan using working holiday, so it's a good idea to get your applications in as soon as the Japanese fiscal year begins in April. Here is a list of the visas that apply to other countries.Visa. Americans cannot obtain this visa but they can get a tourist visa or a working visa for the skilled.
Another visa is the tourist visa which doesn't allow any legal work whatsoever. You're allowed a maximum of 3 months in the country, but this can be extended by doing what's known in the trade as a 'visa run'. This involves leaving the country for a couple of days and then coming back in so that immigration can put another stamp on your passport, and you'll be allowed back in the country for another 3 months. This'll only work 2 or 3 times though. Some people make sure they take a J-girlfriend with them to go on visa runs so that immigration see they're in a relationship and let them through easier (worked for me ;-)). Finding work whilst on a tourist visa is an absolute bastard. I managed it, but I have the luck of the Irish, and I totally wouldn't recommend anyone to take the same risk as me.
Lastly there's the working visa which is reserved purely for the skilled. To get this sort of visa you really need to be a highly qualified tradesman, and even so something like 95% of those with working visas were working in a Japanese company in their home country and were transferred to Japan, or else they had occupied a position in a Japanese company before arrival. Those who can't speak fluent Japanese are pretty much limited to teaching English, which is really the only 'regular' job a non-Japanese speaking foreigner can get in Japan. Like any country in the world, if you're independantly wealthy it's possible to sponsor yourself in Japan indefinitely.
Where there's a will, there's a way.
A word of warning, it seemed to me that the only foreigners I knew who were living in Japan without a degree were those who'd married a Japanese, and they were working some pretty shitty jobs although some were doing okay with their own restaurants and businesses. Obviously if you can speak Japanese with some fluency, the doors are opened wider, but it probably takes around 4-5 years for the average person to gain that kind of fluency in reading and writing, so the only kind of work you'll find until then is likely to be custodial. Speaking Japanese is not an exceptionally difficult task, and Japanese grammar is nearly childlike in it's simplicity. However, learning to read and write in Japanese is a task that requires years of dedication and constant practice, so don't kid yourself if you're thinking "Hell, I'll go on a working holiday visa for a year and when I come back I'll be chatting to the Yamaguchis like a native and writing letters to my old host-family in perfect Japanese". Learning Japanese takes the kind of exceptional dedication that only comes through a true love of the subject, but if you can do it, you will reap the rewards. I would hate for some of you people out there to try to attempt it, and waste 3 years in college before they decide you were never into Japan in the first place, and have to go back to the drawing board. Think long and hard about taking up the challenge guys.