San Francisco and Berkeley are big cities, so a specific location in each city will help us look for your transit options.
SFO (the airport) is not in the city of San Francisco, but about 15 miles south. BART (Bay Area Rapid Transit) goes from the airport to the East Bay but not direct to Berkeley; you would need to transfer. If you have a ton of luggage (are you in the wedding party?) this might be unwieldy.
If you mean San Francisco because you are actually staying in the City, BART does connect San Francisco and Berkeley.
Within both cities, you'd still need to get to and from the BART stations, either by local transit or cabs.
Individual hotels would have to answer the question about shuttles.
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