Downtown is probably the only part of L.A. that one can reasonably cover on foot.
Metro Bus
(http://www.metro.net) is the most extensive bus system in the region. All major streets have at least one and in some cases, several bus lines running daily. Base fare is $1.50 and an unlimited-use day pass costs $5. Both can be purchased on board any Metro bus.
Metro Rail
(http://www.metro.net) is the subway and light rail system for Los Angeles County. Downtown LA can be traversed using the six downtown rail stations that are served by four of the five lines in the Metro Rail system. At the northern end of Downtown LA, the Gold Line stops at Chinatown on its way northeast to Pasadena. The Red and Purple Line subways meet with the Gold Line light rail in Union Station, where connections can be made to buses, Metrolink commuter trains, and Amtrak. From Union Station, the Red and Purple Line subways run along Hill Street, making stops at the Civic Center and Pershing Square, before turning west under the Financial District. There they connect to the Blue Line light rail at 7th/Metro Center. From there the Red and Purple Lines run northwest and west, respectively, and the Blue Line runs south through Downtown LA's redeveloping South Park district, with a stop at Pico, towards the city of Long Beach.
DASH
(http://www.ladottransit.com) is a shuttle service run by L.A. Department of Transportation. When your feet get tired or to better expand your travel area use the DASH. It has several convenient routes that whisk you to almost all of the worthwhile spots Downtown. A ride currently costs 50 cents 25 cents for seniors and pamphlets are available from most MTA stations Union, 7th/Olive and convenience stores Downtown spotty weekend and after-hour service though.