I've never seen a hobbyist do a silkscreen. presumably, since it's possible to make t-shirts at home by silkscreening, then one would assume it's also feasible to do so for your PCB's, but the extra effort required to make the silkscreen mask for every board you lay out is not worth the effort in many cases... if you reach the point where you really need a silkscreen, then you probably ought to be getting your boards made professionally anyway.
with that said, I've heard of people "silkscreening" their board by simply spraying the whole board with translucent green paint, such as that used on toy model kits (ie - Testors brand); apparently if you use the right kind of paint, it burns off under the heat of the soldering iron, so you can solder the board after and only the areas soldered will be exposed, the rest will remain painted. I've never gotten around to trying it, and I'd expect that the burned-off paint could make for some dirty solder joints if you weren't careful, but it sounds possible.