The main place to look for higher-education jobs in Japan is jrecin.jst.go.jp in its English and Japanese forms. Alternately, there are job postings lying around in various faculties of my university (for schools all across Japan) -- which have little to no information. JREC-IN leaves much to be demanded as a website.
First, the English version contains only jobs explicitly posted in English and vice-versa. In other words, you may be missing out on job opportunities if you only search in English (or Japanese). At the same time, maybe you won't benefit from doing both. While I've been applying to jobs on both sides and looking at several. Even for English-teaching jobs, it may be better to just stick to English references as a foreigner.
Second, job postings disappear completely after being filled, so you cannot compile information about what sort of jobs were posted historically or refer back to a job posting. Making matters worse, if a job is modified, then you can no longer find it by url.
Third, if you register your e-mail address and set criterion, the same e-mail address cannot get postings in both Japanese and English -- moreover, it will lock your e-mail address into the initial language you select.
In other words, it is a typical-for-Japan poorly-designed website.
In terms of applying, I've found that many jobs including some for English-teaching (!) are posted only on the Japanese version (see my first enumerated remark above). Conversely, almost all of the jobs posted in English also have a Japanese version. For me, I've been using the two in tandem when both exist to figure out what is meant by sometimes ambiguous English.
Standard fare as to what the job postings contain:
1) request for CV with photo and nationality
2) request for list of academic publications - This is often asked for in a distributed format that splits out categories based on "book", "referred article", and "other". Some schools ask for summaries of articles in English; others in Japanese; others none.
Beyond that, I have also seen:
3) request for a list of teaching experiences
4) request for 1 A4-page teaching philosophy
5) request for references (1 to 3) -- which does not include letters
6) request for a letter of reference which is, unlike in the United States, to be openly included (that really seemed impossible to the graduate placement guy at my PhD-granting institution)
7) request for 1 A4-page research plan
Also, every job posting expects you to mail your application to them by a certain date with the topic labelled in red letters on the outside.
In the vast majority of cases, no e-mail address is provided for questions.