I don't wash my eggs until just before I use them, or just before I put them in clean cartons to sell them. But I do keep them refrigerated from the day I collect them. Mostly my eggs are clean. As @Mrs K said, keeping their feet as clean as possible helps, and I also find that keeping the nests clean is critical. Have roosts higher than the nests so they aren't tempted to sleep in the nests, and change out the bedding as needed. I use shredded paper my DH brings home from the office, it works exceptionally well!
When I do wash them, I put them in my wire basket and just dunk them quickly in warm soapy water. Don't let them sit in water, it will soak into the pores of the shell. Then I quickly rinse under warm running water and check for cracks or flaws. If poop is stuck to them I wipe it off gently with a wet paper towel. Then they go on a clean kitchen towel to air dry. When dry, they go into clean cartons.
The USDA says they are good for 100 days if refrigerated. That's three months and ten days. I write the date they were laid on the big end of each egg so my customers can know they are fresh.
