You must have your x-data interpreted as time. This is done with
set xdata time
set timefmt '%d/%m/%Y'
set xtics 30*24*60*60
set grid
plot 'data.dat' using 1:2
The part set xtics 30*24*60*60
sets the distance between two major tics to be one month. I don't exactly know, how this is done internally, but with the following example file data.dat
01/01/2012 2
01/02/2012 4
01/03/2012 3
01/04/2012 5
the results seems to be correct:
For your requirements you may want to change the format of the x-axis with e.g.
set format x '%b %Y'
to display Jun 2011
...