When was the first Shemita year? I want to compare with our years from 1800 til now.
The first Shemitta year was 21 years after the Jews entered Israel under the leadership of Joshua. According to Seder Olam, that was in the Jewish year 2509 after Creation.
Ramba"m in hilchot shemita veyovel (10:2) says that the first shemita was 21 years after Jews entered Israel (14 years until they captured the land and 7 years till the first shemita), which is 2510 years from the creation. Others rule that 2509 year was shemita.
However there is no contradiction, becuase it depends from where you begin to count the years. The world was created 5 days before the first Rosh HaShono (by the Tana that says the world was created in Elul). And Adam was created at the day of Rosh HaShono. So, if you count from the creation of the world - it is 2510, but if you count from the creation of Adam it is 2509. The Ramba"m himself (the one cited above) gives a hint to two counting methods.
You have to note however that when the second temple was built the count of shemita was reset. So, knowing the year of first shemita is of historical use only and have no influence for us.
For current years, we count shemita from the returning of Ezra to Isreal. Eventually, it happens that if the jewish year divided by 7 have no remainder - the year is shemita. For example current year is 5775 can be divided by 7 without remainder.