I am applying for a job with a new company. They informed me that this will be a "1099" position. When we discuss salary, how much % do I add so that I am not only getting a fair salary but also paying the appropriate Federal taxes? I live in California and what % do I also add for State? Mary

You are independent contractor. The 1099-Misc income is reported on schedule C or C-EZ (Form 1040). You can deduct job/business related expenses. Net income is subject to SE tax at 15.3%.
How you will treat the 1099-Misc income, read: Your U.S. Tax Return: W2 vs 1099-Misc: Employee vs Independent Contractor.

If your position were a W-2 position, your FICA taxes would be 7.65%.

As a 1099 position, the self-employment tax is exactly TWICE that amount, at 15.3%.

BOTTOMLINE: YOUR tax liability is about 8% higher, so your income level should be at least that much greater to compensate.