I received a 1099-Misc for the California Middle Class Tax Refund. I already filed my taxes (fed and state). Had no idea that I was going to receive a 1099. What do I do?

Wait until your return is processed and your tax liability settled. The IRS might adjust your refund or tax due. You can then amend your return. 

The advice from @Bsch4477 is correct, before amending your return you will need to wait until such return has been accepted by the IRS.  You can amend a return only after it has been filed and accepted by the IRS.  E-filed returns are considered filed when you have received notice from the government that your return has been accepted.  If your return has been rejected, it is not considered filed.

Mailed returns are considered filed the date you post your return.

When you are ready to amend to add the 1099-Misc, you can access your previously filed return from the TurboTax home page (in TurboTax online). Scroll down the screen to the section Your tax return & documents.  If you have used TurboTax CD/download, then you can amend your previously filed return by selecting Other Tax Situations, and then scroll down to Other Tax Forms. 

@stefanierees