The foundation of playing clawhammer banjo is the "bum-ditty"
strum. This is derived from the rhythm of the banjo, with each measure sounding like "bum-ditty bum-ditty" or, when counted, "<one>, <two and>, <three>,
<four and>," with the first and third beats of the measure being quarter notes and the second and fourth beats each being a two-part strum consisting of two eighth notes.
I don't want to oversimplify the bum-ditty, as it is probably the single most important
element in playing the clawhammer style, but I don't want to make it sound overly complicated either -- it's not that difficult. Basically I believe it is just a matter of
learning the basic stroke, then practicing it a few thousand times until it becomes second nature. Of course, your practice comes as you are playing your choice of the songs found
elsewhere on this site.