How do I rent my home while I am trying to do a "short sale" on it?

There is really no distinction between renting out your house with or without a short sale. However, if you want to sell the house while there is a tenant living there, first of all, you should disclose this fact to the tenant before you enter into any rental agreement or lease. Secondly, you should be aware of the notice requirements for being able to show the house when it is tenant-occupied. See the section on "When Can The Landlord Enter The Rental Unit" in the DCA guide here: http://www.dca.ca.gov/publications/landlordbook/living-in.shtml