When talking about an event between 1980 and 1989 we call it the eighties. When talking about an event between 1990 and 1999 it is the nineties. But the one from 2000 to 2009 is confusing. Wikipedia was somewhat helpful.
Orthographically, the decade can be written as the "2000s" or the "'00s". Some people read "2000s" as "two-thousands", and thus simply refer to the decade as the "Two-Thousands", the "Twenty Hundreds", or the "Twenty-ohs". Some read it as the "00s" (pronounced "Ohs", "Oh Ohs", "Double Ohs" or "Ooze"), while others referred to it as the "Zeros". The single years within the decade are usually referred to as starting with an "Oh", such as "Oh-Seven" to refer to the year 2007. On January 1, 2000, the BBC listed the noughties (derived from "nought" a word used for zero in many English-speaking countries), as a potential moniker for the new decade. This has become a common name for the decade in the UK and Australia, as well as other Anglospheric countries.
Others have advocated the term "the aughts", a term widely used at the beginning of the 20th century for its first decade.
The "two-thousands" might have seemed good at first, but those using it probably forgot that it refers to the whole millennium and not just the first decade of that millennium. Two contenders make sense - the "Twenty-ohs" and the "aughts". The first is accurate, if three syllables, and the second has historically been used, even if it sounds like you are being told what to do when someone brings up the decade. But one thing is clear - we can't let it be called "the noughties". That would just be awkward.
At least this confusion won't happen in the teens.