I can’t speak to CA, but in my family’s apt in NJ that was built in 1950, they used cable with a ground connection built in and 2-prong outlets.

Basically, you need to test each outlet between hot (shorter prong) and the metal box with a test lamp. Ideally one that draws some power – say a 60W bulb with probes attached – not just a neon probe. If it lights up, then you have a good ground, and you can just use a self-grounding 3-prong outlet, or ground a regular 3-prong outlet to the box using a ground wire.

If not, then it’s a different can of worms, and will be more expensive. You may be able to get away with GFCI breakers and 3-prong outlets (allowed under the Nat’l Electric Code, so long as the outlets are marked as “no ground”).

What kind of wiring is in the house? Plastic Romex? Cloth? BX? Old cloth-and-rubber cable is hideous shite that should be replaced. The insulation tends to fall off if you so much as stare at it wrong.