I just wash them in the sink with a cloth or something. I like to keep my nest boxes very clean so I don't have to wash very many of them.
The ''bloom" on the egg is a hen produced coating that protects the egg from bacteria and dehydration. It's better for egg freshness to retain the bloom which is removed by washing. there are egg washing preparations sold in chicken supply sights. I'm guessing that these would either retain or replace the effect of the bloom. Chicken's dirty feet (mud etc. being tracked into the nest box) and non-nesting activity in the nesting box, such as roosting can lead to dirty nest boxes. One way to prevent mud tracking is make the chickens walk far enough to have the mud off before they get to the nest box. The woodshavings or hay/straw can be replaced in nest boxes whenever they are dirty. Ideally and under the right conditions egg washing isn't needed (or desirable).
