In my case, I joined the Outreach committee, then I moved on to the Israel Education Committee, and meanwhile got involved with the weekly e-mail and bulletin proof-reading. After a couple of years I determined that doing the proofing at home works for me well whereas on-site meetings don't, so I gave up the committee work. One good idea is to ask your schul office about volunteering on a regular or at least semi-regular basis, preferably at the synagogue itself where they will be working alongside other members. Doing a schul-related project will get you in the door so to speak.
Most synagogues have a Saturday morning Torah study. Attendance will increase learning but more importantly from the newbie point of view, it creates a social connection with other members. Being recognized by other members at subsequent events gives a great sense of belonging. Signing up for beginning Hebrew at Lehrhaus is another great connection-creator.
In terms on non-synagogue life: get involved in other Jewish-related organizations, even if it's only a virtual connection via e-mail/web. In my case, I've made donations to the JNF so I get brochures and e-mails from them in return, which creates a sense of connection. I'm also a member of AIPAC and have attended events. I've done the occasional thing with the East Bay Federation. If a new Jew attended one Jewish-related event say every couple of months (outside of synagogue stuff) then he/she may eventually hit on something that sticks for more frequent involvement, and in the meantime will feel connected to the Jewish community by virtue of attendance.
There is also what you might calls add-ons: my e-mail address is my Hebrew name, and my car license plate is personalized to be part of my Hebrew name. These are "constant connections" for me. Also shopping: find a Judaica store like Afikomen in Berkeley or the shop at the Contemporary Jewish Museum in SF.
A very easy way to learn about what is going on in the Jewish community is to sign up for emails. Start with your synagogue, then consider signing up for your local Jewish community center and Lehrhaus Judaica.
If you want to subscribe to a national email try JTA or The Jewish Forward.
Consider volunteer opportunities - Jewish Family & Children's Services or Progressive Jewish Alliance.
Like the outdoors? Look into Wilderness Torah and Urban Adama.
Other fun Jewish venues are the San Francisco Jewish Film Festival and the Contra Costa Jewish Film Festival. There's the Magnes Museum in Berkeley and the Contemporary Jewish Museum in San Francisco.