I went to a hop farm once, part of a conference trip at the NHC in Portland. They cut all the vines down at the same time and lay them into a truck bed, then stripped all the leaves and stems off using a wire thresher looking thing (mostly home-made), then dried the hops on a mesh screen in a big barn with blowers underneath.
As a home grower, I plan to pick off the cones when enough are ready to brew a fresh hop beer. Hopefully I'll be able to do this for two batches, but so far I haven't seen any cones. I really want a fresh hop beer......