Karl,
Sorry it took so long to answer your question. This is a very difficult question to answer because a lot depends on your visa status and any special qualifications you have.
If you have technology related skills, you will probably be able to find some non-teaching jobs. However, if you're like me, without any special skills, your fields of available work will be more limited.
Concerning the job market for non-Japanese speaking foreigners, English teaching and technology related jobs are your best bet if you don't have a spouse visa. If you've got a spouse visa then you will probably be able to find an unskilled labor job even if you don't have any special skills. I've heard of many people who couldn't speak Japanese starting out life in Okinawa working at moving companies.
The other option is on-base work. There are several types of jobs on base and I'm not much of an authority on them, but from what I understand, most of the local hire jobs require you to have a permanent residency or spouse visa. There are also many US Government employees on base, but I think you probably need to have permission to work in America for these jobs. There are also contractor jobs available, and some of these may not require you to have permission to work in America. The truth is though, I'm not sure.
In regards to your second question, the first thing you need to work in Japan is a work visa. Most work visas require some kind of sponsorship and either work experience or a 4 year university degree. The
Japanese Ministry of Foreign Affairs website explains the different visa statuses more thoroughly than I could ever hope to.
Most people that teach English are on a Specialist in Humanities/International Services visa. This visa requires a 4 year degree and a company to sponsor you. With it you can engage in these work activities:
Activities to engage in service that requires knowledge pertinent to jurisprudence, economics, sociology, or other human science fields. Activities to engage in service that requires specific ways of thought or sensitivity based on experience with foreign culture, such as interpreting, translation, copywriting, fashion design, interior design, sales, overseas business, information processing, international finance, design, or public relations and advertising based on a contract with a public or private organization in Japan.
Once you start working you have to pay income tax which comes to about 3% of your salary. It used to be higher, but recently the government reworked the tax laws. In addition to paying income tax you are require to have some kind of insurance to be a legal worker. Technically you have to be enrolled in one of the two National Health Insurance schemes. Either
shakai hoken (Social Insurance,provided by your employer) or
kokumin hoken (National Insurance, available through the city office).
When enrolled in
shakai hoken you will automatically be enrolled in the
nenkin (pension) system as well. This will cost you about 15% of your salary. If you have
kokumin hoken it will cost around 6,000 yen per month for the first year, then about 10% of your salary after that. Sometimes the city hall may force you to register for the
nenkin plan with
kokumin hoken though, and in that case, you will be paying 20% or more of your salary.
There is another option though, and that is to get a private 'travel insurance' plan. Many people choose this option because of the low price, 5,000-10,000 yen a month. Although technically doing this is not allowed, as far as I know the government doesn't try to force foreign residents to join one of the national health care plans.
One more thing, once you've completed one calendar year in Japan, you will have to start paying
shimin zei (city or ward tax), which is based on your previous year's income. This ward tax runs about 60,000-80,000 yen a year and is payable in 4 installments. (This tax will probably be going up though, because the national income tax has gone down).
If you have any more specific questions, I'll do my best to answer them.
John