Most shorts these days have synthetic chamois (the real kind comes from a kind of goat leather). Synthetic chamois are washable. You should not have any problem just throwing them into the washing machine on gentle cycle. They can also go in the drier at a low temperature.

If you want to be really careful, you can hand wash them with woolite or campsuds in the sink. Rinse, ring out and hang to dry. They usually dry over night.

It is a good idea to wash shorts after each and every ride.