Contextually, whenever decades are referred to by their last two digits, they refer to decades that have occurred in the last 100 years. As you've already noted, 90s is read as "nineties", 80s is read as "eighties" and so on. However, unlike those decades, there isn't a clear consensus as to what to call the 00s.
Some of the terms used include the "noughties" (deriving from the British name for the digit 0), "aughts" (an archaic word meaning "nothing at all", referencing the double 00s) as well as "two thousands" (deriving from the fact years from 2000-2009 were often referred to as "two thousand and number").
Personally I read it as "two thousands", but as far as I know there's no clear accepted standard.