Try doing a google ssearch for the Oakland airport web site. Many airport web sites list ground transportation options and costs.
Oakland airport to SF by cab will run you around $70. Shuttles can add up if you have lots of people, so my family of 4 always takes a cab.
If you don't mind taking public transportation, I would suggest taking BART (a light rail type train) from Oakland Airport to downtown San Francisco. If you get off at the first stop in SF, which is "The Embarcadero", you can then catch a cab or take the street car to Fisherman's Wharf.
If you prefer just to take a shuttle, I would go directly to the airport's website, where they most likely provide information on the specific companies that service their airport.
If you're arriving mid-day (not rush hours) I would take BART, there is a shuttle bus from OAK to BART, you buy the tickets at a machine by the bus stop which is on the platform in the middle of the street in front of the arrivals area. At the BART station, you buy tickets for the ride to the Embarcadero station in SF. Go up to Market Street and look northeast for the Hyatt Regency Hotel. There is a taxi stand in front of it.