Pick a hole in each end, stir the contents, blow the contents out, rinse the inside.
I'm not sure whether any product besides water is used to rinse them. I'm sure there are directions available.
I watched my grandma do this a LOT. She did lots of crafts with egg shells. I still have quite a few (both finished crafts and empty eggshells.) Many, many years later, they are still clean and mold free and don't smell.
I recommend practicing on eggs that you don't care about. I broke quite a few in learning how to blow them. The smaller the holes, the less likely they are to break and the better they look. But it is harder to stir the contents and harder to get the contents out.
The older the egg is, the easier it is to stir and to blow it - it isn't rot (although they may also rot especially without the bloom). It is because the membranes between the layers of egg gradually lose their strength. It is the same reason fresh eggs straight from your coop will stand higher in a frying pan than eggs from the grocery store.