The available websites, www.metro.net, and the Metro Trip Planner on www.experienceLA.com are helpful if you know your starting and ending Metro stations, but if you try to use addresses, they can be very confusing and don't necessarily give you the best solution. It may route you on a slow bus to an exact address, when you could take a fast train that stops a couple blocks away.
I've tried to use the 1-800-COMMUTE phone number to get route information, but have never been able to get through to anyone. I've had better luck calling the local transit service for my starting city. A real person responded and was able to give me an exact timetable and route including the local bus and the Metro schedule and route. Here is a list of Local Transit Services Around LA.
Google Maps also includes a public transportation option, but since it's based on the Metro's own system, it has the same issue of adding unnecessary bus legs to drop you right in front of your destination that make the route slower than if you took the train one more stop and walked 2 blocks to your destination. Since Metro train stops are marked on the map with an M, be sure to scan the area around your destination to see if there's a closer stop than the one Google recommends, and if it's on the same line you'll be traveling, way the added time of transferring to a bus and the number of bus stops with the distance you would have to walk. If there's a closer station, but it's on a different line, you probably won't gain anything by changing trains rather than transferring to a bus.
Tip: When comparing train distances on a map, take into consideration that underground trains, such as the Red Line, are much faster than over-ground trains, like the Blue Line, which have to stop at traffic signals.