No one knows for sure.
High school students learns less than 1,000 words.
A college student probably has a vacabulary of some 4,000 words.
Good newspapers equivalent to the New York Times use perhaps 2,000 words.
To read or write Chinese by computers, each word is coded by
a number, just as English alphebets are coded in ASCII.
One such standard code, called the GB code, has about 2,000 words.
On the Internet, there are a number of Chinese word lists you can
easily access. These contain anywhere from 3,000 to 138,614 words.
These are of interests to scholars mostly.
Word lists by Chih-Hao Tsai