Spouses of Japanese nationals can obtain spousal visas, which carry no restrictions on employment.
The Working Holiday program is open to young citizens (between 18 and 30) from Australia, New Zealand, Canada, South Korea, France, Germany, Ireland and the UK: those eligible may apply for working holiday visas without having a job offer.
The most common form of employment among foreigners is teaching English.
Many foreign residents from English speaking countries now work in Japan, most as language instructors. The demand for native language instructors remains high, with a lot of major language schools now operating recruitment offices overseas. It is quite easy to find work teaching in Japan as there are many eikaiwa (conversation schools). The most famous being Nova, GEOS and AEON. I recommend teaching in Elementary or JHS with an ALT company as this is the most rewarding.
Other fields that qualified residents have a good chance to find work include translation, IT, modeling and entertainment.
The best site to look for employment in Japan is Gaijinpot.
How to become an English Conversation Teacher