San Mateo County Transit (Samtrans) has Route KX, an express bus from the airport to downtown San Francisco and costs $4.00.
It runs from 5:50am to 10:37pm every 30 minutes, from 7:20am to 9:30pm weekends. Route 379 is the overnight bus using the same route. These buses only accept limited amounts of luggage, so if you have a lot of bags this is not the best option.
Route 292 is a local bus to downtown San Francisco and costs $3.00. This bus runs from 5:30am to 12:40am every 30 to 60 minutes.
Buses run from the lower level (Level 1) of all terminals- just head downstairs and follow the signs for ground transportation.
All buses will stop on Mission Street downtown, get off at Mission and 5th- see map below for further details.