In looking for work anywhere, connections matter. When I was younger, I worked a summer for a company called Indy Office Solutions -- now Sharp mainly due to connections my parents had with the owners through church. This job paid pretty well for the times and was far better in terms of the type of labor.
At the same time, I probably would have been able to find something on my own. This is largely because the US job market for both academic positions and regular jobs is largely open. Real jobs are posted every day on Monster, craigslist, the CHE, and disciplinary websites like the apa-online and philjobs. And while I connections can give a boost, many people are hired entirely without connections involved.
Japan does have such a system -- for its own college graduates. While I hope to write more on this later, the Japanese system for higher education has only a passing resemblance to the American system from which I came. Based on the ranking of a student's university, they can find work and get interviews for open positions. The interview portions itself largely tests personality and the written 履歴書 evaluates the credentials and acts as a filter. Potential employees will be asked personal questions about whether they are married, how old they are, how long they plan on working for the company, and whether they have children. Also, the date of birth will appear and a picture (no matter the job type).
But I digress. As a foreigner trying to work in academia in Japan, you have zero access to this completely open employment system. The academic job market in Japan is ... rife with cronyism, jingoism, and little fiefdoms. Foreigners are shielded from some of this, but the job market still greatly depends on connections. Thus, a key task is to tell everyone you know that you are looking for work and put out the impression that you would be a pleasant (and competent) co-worker.
In my own case, I told my adviser and a friend who both teach here that I was looking. I did so by asking them for advice for the job search, but beyond mere advice, I was also asking so that they would know I want to find a job and provide me with connections if possible. Through this, I may have one opportunity to teach next semester on Mondays not too far away. While that's just one opportunity, every job that I currently do here has involved some initial hiring for one thing followed by expansion to other things.