How to determine encoding for file?

[kj]

I've downloaded a large file that is supposed to contain a mixture
of Japanese and English (it's basically a learner's dictionary).
The English is displayed correctly, but not so for the Japanese.

I've tried setting the buffer's coding system to utf-8,
japanese-shift-jis, japanese-shift-jis-mac, japanese-shift-jis-dos
(just guessing).  None worked.

In fact, I'm not even sure that any of these changes of the coding
system achieved *anything*, since the buffer's appearance remained
unchanged throughout all this mucking around.  I used the command
set-buffer-file-coding-system to do this.  Should I need to do
anything besides re-setting the coding system to see a change in
how the file is displayed?

More importantly, is there a better way to determine a file's
correct coding system besides trial and error?

TIA!

~K