1.  1900: 'nineteen hundred' 

2.  1901: 'nineteen oh one' (more common and informal way of saying 1901) or 'nineteen hundred and one'

3.  2001: 'two thousand and one'

4.  2010: 'twenty ten' (more common and informal way of saying 2010) or 'two thousand and ten' (less common)

5.  1990 to 1999: 'nineteen ninety to nineteen ninety-nine' or this whole decade is known as "the 90's"

6.  1901 to 2000: this century is known as the '20th century'

7.  2001 to 2100: this century is known as the '21st century'

For figuring out the centuries, you add 1 to the first two numbers of the current century you are talking about. For example, the years 1801 to 1900 would be the 19th century since 18+1=19. The 19th century can also refer to the years 1800 to 1899.

I hope I answered your question to your satisfaction. Let me know if you have any other questions and feel free to check my profile if you are interested in taking a lesson.