The main files for the data are

5873inv.txt - list station numbers, lat/lon/elev, station name

12 files stnx1.txt-stnx12.txt - each row contains one month's data for
one station. -1 is used as missing value code (note this includes, for
example, always giving the missing value code to September 31, but there
are also a lot of genuinely missing values in these datasets).

The way I use these files myself is to run a Fortran program "decode" 
that expands the station files into 5734 individual station files -
that takes up about 3GB but is a convenient format for direct loading
of individual data series into Fortran or R (or any other programming
language that reads data directly from ascii files).

I have included a compliled version of "decode" for Windows (if you copy
this, need to copy the "salflibc.dll" program as well - it's based on the
free online version of the Salford systems Fortran compiler) but I have
also included the program code (decode.for) in case you want to compile
it on unix or linux. The way you use this is very simple: in Windows just
open a command window and type "decode". The program then creates all the
new data files (takes 5-10 minutes on my machine).