Flight
If you fly into SFO, taking BART (Bay Area Rapid Transit) into Oakland is cost-effective (~$10.00) and relatively easy. There is a Bart station accessible from the airport, and any Richmond, Antioch, Pittsburg/Bay Point, Pleasant Hill, or North Concord train will get you to the East Bay. From there, I'd recommend hopping off bart in Downtown Oakland and getting a Lyft or Uber to your place if you're staying in Oakland. If you're staying in Berkeley or elsewhere and have questions about using Bart most efficiently don't hesitate to reach out! Alternatively, an Uber or Lyft to the East Bay will run approximately $50.00 depending on timing.
Flight
If you fly into the Oakland airport the easiest mode of transportation to your hotel/AirBnB will likely be Uber or Lyft (~ $20.00 depending on timing and exactly where you are headed). Alternatively, you could take Bart from the airport to the Oakland Coliseum station, then switch to a Richmond train to head towards downtown Oakland (~ $8.65 to exit at 12th Street (Downtown Oakland station)).