I’m 65 years old and collect Social Security and live in California. Do I need to pay federal or state taxes

If the only income you receive is your Social Security benefits, then you typically don't have to file a federal income tax return.

California also exempts Social Security retirement benefits from taxation. 

If Social Security is your ONLY income you are not required to file a tax return unless you have a 1095A for marketplace health insurance.   If you have other kinds of income in addition to the SS, you might need to file.  Do you have other income---from still working, from investment accounts, from a retirement account like an IRA or 401k, rental income, gambling income....etc.etc.etc.?

Who has to file?

http://www.irs.gov/uac/Do-I-Need-to-File-a-Tax-Return%3F