I keep my nestboxs very clean, so dirty eggs are a rarity to start with. If I do occasionally get a very dirty egg, it's fed to the dogs. Those with slight blemishes or dirt are stored unwashed, so as not to remove the bloom. The bloom keeps dirt and bacteria out and eggs with the bloom intact stay fresher much longer.
I wash them right before using by giving them a quick rinse under running very warm water, then use a paper towel to dry. Washing in cold water or water colder than the egg itself causes the contents of the egg to contract, pulling dirt and bacteria into the interior of the egg.
Soaking the eggs in water or water mixed with detergent is a big no-no. As soon as you submerge the eggs the dirt on the eggshell gets released into the water and then sucked into the eggs as the contents contract.