Mine lay wherever they happen to be when they get the urge, unless they are getting ready to pretend to be broody, in which case they will hide them in a corner somewhere. They are nearly always filthy.
For eating eggs, I just run them under water and use a rubber scrub brush until they come clean. Takes a little effort, but it does a good enough job. Use warm water so you don't drive bacteria through the pores.
For hatching eggs, I'm much gentler, but I have still been cleaning them. I use warm soapy water and alternately dunk & rub (gently) with my hands until they are clean. BUT, I have only had 69% hatch rates, so next time I am going to try incubating them without washing... should be interesting... it seems counterintuitive to me, because they are SO filthy, but several experienced folks have suggested it, so I'm going to try.