This is the dating system which is most commonly encountered on the nakago of Japanese swords. In modern times as each emperor takes the throne, his reign is given a name which is represented by two kanji. In older times an emperor might give names to several eras or reign periods within his reign. Also he may continue to use a reign name given by his forebear for some time after his accession to the throne. Reign periods or eras therefore, do not necessarily correspond directly with the reign of a particular emperor.
The year-date is simply measured as a year count from the beginning of the relevant nengô or reign period.
As an example the EISHÔ reign period began in the year 1504 CE.
It is represented by the kanji 
If on a blade the date is shown as EISHÔ 12 NEN 
then this simply means (assuming it is not gimei!) that it was made in the twelfth year of the period EISHÔ.
Note that as reign periods have no year zero, the correct way to calculate the western equivalent date in this case is to take the beginning year of the reign (1504), add the 12 (=1516), then subtract 1 (=1515). So EISHÔ 12 = 1515 CE.
An exception to this numbering system is the first year of each era. The
first year of any reign period is called GANNEN 
so the first year of EISHÔ would be represented as
Also note that between c.1332 and c.1392 CE there were two courts (Northern and Southern) ruling Japan, so for any given year in this period there are two separate nengô.
A full Nengô List covering TENKI 
(1053 CE) to HEISEI 
(present day) is available.
Occasionally following the nengô and the year number, is another
number followed by GATSU 
and HI 
.
This is the number of the month and the kanji for 'day'.
A full date inscription on a sword nakago might read as follows:
Tenpô jûsan nen ni gatsu hi
This translates as "A day in the second month of the thirteenth year of Tenpô"
You can see from the Nengô List that the Tenpô reign period began in 1830 CE, so adding 13 and subtracting 1, the western equivalent date for this blade would be 1842.
Instead of a month there may be one of the kanji indicating the season, together with HI . This would translate as " A day in spring/summer/....."
For practice in reading Japanese Nengô dates see the Practice Date Inscriptions Page
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