I took the Flyaway from LAX (See ExperienceLA Spotlight: Go Metro: Flyaway Bus Service Between Union Station and LAX) just this past weekend and was glad at the ease in using the service.
The LAX/Union Station Flyaway opened a few months ago (for those in the San Fernando Valley, there's also a Van Nuys/LAX Flyaway that's been in existence longer) and it's an affordable and easy way to travel to-and-from two of Los Angeles' main transit hubs. The fare is only $3 dollars one-way ($6 roundtrip). Metro currently estimates the route's driving cost at about $11.29 (based on AAA's formula at 56.2 cents/mile).
Once you're at Union Station, you can roam onto Metro's major transit lines to get to any number of great Southern California destinations.
-ExperienceLA Web Coordinator