Begin with this basic graphical pattern:

e---------
B------o--
G----o----
D--o------
A---------
E---------

Play the pattern repeatedly, increasing by one half-step each time.

e---------------------------
B------5-----6-----7-----8--
G----4-----5-----6-----7----
D--3-----4-----5-----6------
A---------------------------
E---------------------------

Once you are able to play it all over the fretboard, start concentrating on picking technique.

I've been working with the dimished scale lately, and I thought it might be a good idea to document how I wrap my mind around it.

First off, let's start with a diagram of a diminished scale:

The black dots represent the chord itself, while the grey dots are alternate locations to play notes of the chord. As far as fret numberings go, if you wished to play the Bb diminished scale, you would start by placing that first note at Bb, or the sixth fret. However, due to the "overlapping" nature of the diminished scale, you would also simultaneously be playing in the D, F, and Ab diminished scales.