You have many options when traveling to the Bay Area.
If you are just coming for the wedding and want to minimize costs, you may want to fly in and out of Oakland International Airport (OAK) and stay in Oakland (since the wedding is in Oakland).
On the other hand, if you intend to stick around (and the Bay Area is beautiful in the summer), you might want to stay in San Francisco (where more of the attractions for out-of-towners are) and thus fly in and out of San Francisco International Airport (SFO).
You can look for flights on your favorite travel site, but note that there are good airlines that don’t show up on sites like Orbitz (since they don’t partner with other airlines). Southwest Airlines flies into both OAK and SFO and is recommended for both price and service. JetBlue also flies into both airports.
See also “Where to stay” and “The wedding itself” (for how to get there on the actual day).