Sterilize the egg when you first get it and after each use. You have a couple of options in how to go about cleansing it hygienically: You may want to boil water, then remove the water from the stove. Let the water cool for a bit, you should be able to put finger in it. Set your egg in the water for 12-15 minutes. DO NOT PUT YOUR EGG IN BOILING HOT WATER!
Second option is to use a mild organic soap such as Dr Bronners.
To cleanse your egg energetically, you can wave it under the smoke of sage, bury it in soil within the earth, add to a bowl of salt water, as well as putting it under the Full Moon light.