511
The number One thing to remember about getting arround in the Bay Area is "511". You can call it free from anywhere in the nine counties and get public transit information
Bart
The main commuter train system in the Bay Area. The "12th street Oakland City Center" stop is right next to the hotel. Use ticket vending machines to purchase reusable (but disposable) mag-strip tickets which must be scanned on the way in/out of the stations. Costs vary based on how far you travel.
Taxi Service
Taxi's are fairly prevalent in Oakland (and the rest of the bay area), but unless you are starting at a major taxi stand (ie: big hotel, airport, major bart station, etc...) you will have to call one to come pick you up.
It's worth carrying the numbers of some taxi companies with you if you plan on going out...
http://www.yelp.com/c/oakland/taxis
Going to San Francisco
The easiest way to get to (and around) SF is to ditch the rental car and take Bart (parking is a nightmare in SF, even in the residential areas). If you want to go somewhere in SF that isn't near a bart station, transfer to MUNI, or hail a cab near on of the downtown Bart stations. (Taking Bart to SF and then hailing a cab is much cheaper then trying to take a cab from Oakland to SF, even with 4 people)
http://www.sfmta.com/cms/home/sfmta.php
Getting To/From Airports
OAK: http://www.flyoakland.com/ground_transportation.shtml
SFO: http://www.flysfo.com/web/page/tofrom/transp-serv/
Bart trains go right up to the international terminal at SFO. For OAK you have to pay a few dollars to ride a little shuttle bus to the nearest bart station...