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About Japanese Calendar Years
Nengo: Emperor Eras
The Japanese year is written with the name of the reigning Emperor followed by the year of his reign and the kanji character for "year" (nen). For example, 2005 is Heisei 17, and can be written in Japanese as 平成17年 or 平成十七年 (17 is 十七, juu-shichi, or 10 and 7).
Pictured here are two Japanese coins. The 100 yen coin is inscribed 昭和63年 (Showa 63), which is 1988. The 500 yen coin does not mix Japanese kanji with Western numerals: 平成十五年 (Heisei juu-go, or Heisei 15), which is 2003. (option: see the large image)
(Can you see the "watermark" visible at this angle in the zeros on the 500 yen coin: 500円, 500 yen.)
Gannen, the first year of an Emperor Era
The first year of an Emperor era is called gannen instead of ichi nen. The characters for gannen are 元年. So Reiwa 1 is 令和元年, not 令和1年 nor 令和一年.
Note that the gannen (first year) is generally not a full year long. For example, Showa 1 started December 26, 1926, and Showa 2 started a week later (January 1, 1927). Also note that the Japanese calendar years increment by one every January 1st (the same as the Gregorian calendar), not on the anniversary of the Emperor's reign.
Calendar Years in Japan
Currently in Japan, both the Gregorian calendar years (e.g., 2004) and Japanese nengo are used. The Gregorian calendar has been used alongside the Japanese nengo since 1873. Regardless of the system, Japanese dates are written in the order of year month day.
Sometimes the kanji for the eras are shortened. For example, paperwork forms that require your date of birth will give you an option to choose Showa or Heisei; this choice may only show the first character of each era, or it may even be a choice between alphanumeric S and H.