For most visitors the hub of transportation will be either the Downtown Santa Fe Train Depot or the Old Town Transit Station, which is on the rail line north of the Santa Fe station.  A map of the downtown area transit connections is available at this website as of December 2011 ; further information is available at 619 233-3004.

The Downtown Santa Fe station is the end of the line for the Amtrak trains that go between San Diego and Los Angeles; a couple of trains daily will also continue north past Los Angeles into Santa Barbara and San Luis Obsipo.  The downtown Santa Fe Station is also the southern origin for the north coastal Coaster train and the Blue and Green Trolley lines.  One short block east of the Santa Fe depot is America Plaza station which is a transfer and departure point for the Blue and Orange Trolley lines.  Many buses also are within a block of the Sana Fe station, including the #992 bus to/from the airport, as are the cruise ship terminals.

From Old Town station, which itself is a popular tourist destination, you can get the San Diego Trolley to go downtown, the gaslamp, Tijuana, Qualcomm Stadium and east county. The trolley is a safe and fun way to travel in San Diego. Tickets are available at self-sevice kiosks at each station. If you're only going one direction on the public transit, you will have to pay for each bus you take, they no longer issue transfers. Your best bet, though, is probably to buy a $5 Day Pass which works for both the Trolley and buses all day.  You can buy it from any bus driver, but if you don't already have a "Compass Card" (which you probably don't as a tourist), you'll have to pay $2 extra.  Your Compass card can be reloaded and can even be loaded with a regional day pass ($12) that allows you to also take Amtrak, COASTER, SPRINTER, BREEZE trains north and east of the Pacific Coast highway.  It is a great valley and uses microchip technology to tap and track usage. 

From the airport you can catch the #992  or #923 bus which will take you into downtown as well as the Santa Fe depot.

From the Old Town Transit center you can also take the bus to get to Sea World(#9), Mission and Pacific Beaches(#30, as well as La Jolla( #30). The #6 runs from Hotel Circle to the Old Town Transit Center. 

You may be staying in Downtown San Diego, since there are numerous hotels there with a range of room rates. Some of these transit lines can be caught in Downtown San Diego--notably the #30 to Pacific Beach and La Jolla, and the Blue Line trolley (Old Town-Mexican border via Downtown). From Downtown you can also catch bus line 3 to the lively, urban Hillcrest neighborhood (catch it on 5th Avenue).To go from downtown to other destinations--like Sea World--you will need to transfer at Old Town.

To get to Balboa Park and the San Diego Zoo, take Orange or Blue Line Trolley to the City College stop, then grab the #7 bus on Park Blvd going north to Balboa Park.

You can also use their Trip Planner function.

To avoid confusion, you should know that there is another "trolley" service in San Diego. This is called the Old Town Trolley, and is a private bus service which visits many off the major tourists sites in San Diego in a loop route.  One can purchase a day ticket, and get on and off the trolley at your leisure. While it also departs from Old Town, it does not leave from the Old Town Transit Center.