The LA Metrobus system is pretty good; check out their website (http://www.mta.net/) and download maps (http://www.mta.net/riding...) and route schedules (http://mtaweb5.mta.net/). With the addition of the Santa Monica Blue Bus and the Culver City Bus, the Westside is fairly well covered.
In the West Los Angeles area the Santa Monica Big Blue Bus (http://www.bigbluebus.com...) is a very reliable and well-maintained bus service. Additionally, their website has a great flash based interactive map (http://www.bigbluebus.com...) along with a standard map (http://www.bigbluebus.com...). The Culver City Bus system is accessable via their web site (http://www.culvercitybus....) maps and schedules.
During the summer months, there are various beach shuttle services available during the weekends; there is also the Park Link (http://www.parklinkshuttle.com) service for the Santa Monica Mountain parks and beaches which carries both passengers and up to 3 bikes per shuttle.
For ultimate convenience it is best to rent a vehicle. Most of the majors are available at LAX airport.
