Actually, clawhammer (also known as frailing, rapping the banjo, down-picking, and even "that club-fisted way", is like this:

Instead of picking the strings either with a flatpick (as in tenor or plectrum banjo) or by the palmar surface of the finger picking the string, in clawhammer (and other names) it is the nail side of the finger (usually index or middle) that strikes the string. This is done without flexing the finger. Rather, the whole hand (sometimes the whole forearm) moves up and down, to bring the picking finger into contact with the string. By the same motion, the thumb is brought in contact, alongside the shorter string called, surprisingly enough "the thumb string." The thumb does not flex to pick the thumb string, but the upward return movement of the hand brushes the thumb against the thumbstring (also called the chanterelle), sounding it on the off-stroke.

There are further string-sounding techniques, such as hammering-on, pulling-off, double-thumbing, and drop-thumb, but the previous description really tells the basis of clawhammer.

Dave Oesterreich