When we did the eggshell mosaic many years ago, we simply let the eggshells sit in a sinkful of water that had a squirt of regular old dish soap in it! There - how's that for a formal and complicated procedure! You don't really have to "wash" them each individually if you toss them into sudsy water right away. Let them soak for a while in rinse water too, then spread them out onto a towel to air dry. Store them in an open tupperware container - or in an open shoebox so that you can add to your stash as you clean and dry more on other days. Don't worry too much about cracking them, because they will need to be around the size of a pinto bean for this
project anyway - only they won't have regular shapes - that's what makes the project so cool-looking when it is finished - each piece sort of has it's own unique shape, but together, they make a whole design! If you don't soak the shells the same day, the egg dries on the shell and it is harder to remove, but each person will have to do what is more convenient for them. We did this project in the winter, so Ryan's mosaic is an outside scene of an evergreen tree with snow falling lightly around it - it's beautiful.
Hope this helps!