I hope this is a question appropriate for SO.
The article in question: http://www.nytimes.com/2015/01/25/opinion/sunday/seth-stephens-davidowitz-searching-for-sex.html
As far as I can tell, the only publicly available data from Google Search is through their Trends API. The help page states that
The numbers on the graph reflect how many searches have been done for a particular term, relative to the total number of searches done on Google over time. They don't represent absolute search volume numbers, because the data is normalized and presented on a scale from 0-100.
However in the article, the author reports (absolute) "average monthly searches". The source is stated as:
All monthly search numbers are approximate and derived from anonymous and aggregate web activity.
Source: analysis of Google data by (author)
So, how did he get this "anonymous and aggregate web activity"?