What was done
The authors reviewed existing global precipitation data sets and analyzed the information they contain to obtain a picture of precipitation patterns over the 20th century.

What was learned
Precipitation over the land area of the globe was mostly below the century-long mean over the first decade and a half of the record but increased, according to the authors, "from 1901 to the mid-1950s, remained above the century-long mean until the 1970s and then declined by about the same amount to 1992" (taking it well below the century-long mean), after which it "recovered towards the century mean."  Hence, for the entire century, there was a slight increase in global land area precipitation; but since 1915, there has been essentially no net change.

For the oceanic portion of the world between 30°S and 30°N (which record begins in 1920), there was, in the authors words, "an overall decrease in tropical ocean precipitation (~0.3% per decade)".  Hence, for the world as a whole - which is 70% covered by water - there may well have been a slight decrease in precipitation since about 1920.

What it means
Essentially all state-of-the-art global climate models predict earth's hydrologic cycle should be enhanced by rising atmospheric CO2 concentrations.  However, since 1920, when the air's CO2 concentration stood at 300 ppm, until now, when it is about 370 ppm, there has been - if anything - a decrease in global precipitation.  What does this observation tell us about the climate models?  It sure doesn't vindicate them!