I received several thousand dollars worth of stock as an inheritance. I live in CA. If I sell them, what is my tax liability & how is the IRS notified that this is an inheritance?

Any thing (money and property) you receive as gift or inheritance, you (the receiver) don't pay any federal tax. Also CA does not tax on inheritance (you should recheck on CA web site).

Your cost basis of the stocks is the valuation (Fair Market Value) of the stocks at the date of the decedent's death or the FMV (Fair Market Value) on the alternate valuation date if the personal representative for the estate elects to use alternate valuation. When you sell the stocks you will report the sale on schedule D of Form 1040. You have profit only if sell the stocks at price more than your cost basis.

Well researched and totally accurate.

I have nothing to add.