Ride BART - Bay Area Rapid Transit
BART has one of the highest on-time performance records in the nation (unless they shut the system and internet down to prevent public protests), but do give yourself a little extra time in case you miss a transfer or encounter an unanticipated delay. Use BART's trip planner to look up BART times and to download the convenient printable version to take with you.
From San Francisco Airport:
Take the Pittsburgh / Bay Point bound train
@ the Macarthur station, transfer onto the Richmond bound train
@ the Downtown Berkeley station, exit.
Walk 2 blocks East towards UC Berkeley Campus.
From Oakland Airport:
Get on the Bus called AirBART
@ Coliseum/Oakland Airport Station get off the bus.
Take the Richmond bound train