What was the first computer to support Japanese script, not just as a toy demo, but at a level where you could actually use it to get a day's work done with Japanese documents? And how did it do it? I can see how to do it when you have megabytes of memory and a megapixel display, but I'm curious just how early it was done.
I don't know what the first computer to support Japanese script was. If only supporting Japanese kana counts, then it was probably some mainframe computer in 50's or 60's connected to a Japanese teletype. However the first non-toy Japanese word processor that supported both kana and kanji was apparently the Toshiba JW-10 which first shipped February 1979. (There was an earlier prototype word processor made by Sharp, but it doesn't seem to have gotten past that stage.)
The JW-10 was big and expensive, the size of the desk and it cost ¥6,300,000, or $31,000 US at the exchange rate of the time. It's display used a 24x24 pixel font and printed documents on a 24-pin dot matrix printer. For kana to kanji conversion it came with a dictionary of 54,000 words and 8,000 proper nouns (eg. names) that could be expanded with 10,000 user-defined words and 8,000 user-defined proper nouns for a total of 80,000 words.
Here's a picture of the JW-10 taken from the IPSJ Computer Museum web site:
Note that according the IPSJ's page on the JW-10, at the time it was release "katakana were the only Japanese letters handled by computers (except for some systems using special equipment)". So there would been some earlier computers that supported kanji, but wouldn't have had the novel kana-kanji conversion, an early input method editor (IME), developed for the JW-10.
Early Japanese personal computers(like NEC's PC-8000) had expansion Kanji-ROMs sold separately.
The computers themselves only supported JISX0201(7-bit ASCII and half-width katakana) natively and required additional software in order to support the extra characters.
I can't find any reference regarding the first out-of-the-box input method but it seems to have happened around the introduction of 8086-based PCs(NEC PC-100 and PC-98).