The Wikipedia entry to folding has a pretty picture and it is how I imagine it. But at this level, far below the wavelength of visible light, it must be much prettier! Like a colourful rope made out of very tiny vibrating strings perhaps.
The next picture shows how scientists imagine these things on even lower levels, again it is from Wikipedia and it is from the entry to the string theory. 1-4 should be obvious and 5&6 show quarks and strings:
I should also mention that there is a competing project called Rosetta@Home that deals with prediction and design of protein structures, but they seem to be doing nothing but to produce pretty pictures ...
