By Train / Bus, San Jose

Caltrain will take you to or from San Jose and runs as far south as Gilroy and as far north as San Francisco. This is a great option to get to SF if you don't have a car. As the train goes north toward SF it stops in all of the major cities along the peninsula (west side of the Bay) so it's a great way to visit those cities as well. If the Airport is your destination you can now take the train to Millbrae where it will connect with BART which now runs to the airport.

Public transportation in San Jose and much of the rest of Santa Clara County is served by the VTA (Valley Transport Authority). The VTA operates many bus routes that go up and down the length and scope of the valley, as well as a state-of-the-art light rail system, whose hub is in downtown and connects to the city's surrounding neighborhoods and major coroporate compounds.

Fares are relatively inexpensive.

Good luck getting around San Jose without a rental car. This is a very public transportation unfriendly town.
Few cabs, bus schedules are inconsistant and take you through some sketchy areas and the newer metro lines just don't service the entire area yet.
It is like San Jose planned out a bad idea and ran out of money halfway through.
Rent a car, your best way around town. Parking is ok downtown, especially in evenings and weekends - most parking structures are free to get people to come downtown.

I travelled to San Jose via the train, but flying there would probably be significantly faster.
Since San Jose is sprawling (it's bigger than San Francisco), driving is the best way. However, a nice way to get to San Francisco from San Jose is via Caltrain, a commuter rail service that runs between the 2 cities, and cities along the route like Palo Alto. The station in San Jose is across from the San Jose Arena.

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VTA Light Rail service is one convenient way to travel around San Jose, especially if you want to go from one end to the other end of San Jose.