Just west of San Jose, Santa Clara is adjacent to San Jose Mineta Airport SJC.
By train
Caltrain stops at Santa Clara Station, on the east side of Santa Clara University 1001 Railroad Avenue. Though Caltrain doesn't really stop at San Jose Mineta Airport, the free Airporter bus VTA line 10 shuttles passengers between the airport and the Santa Clara Caltrain station.
The Altamont Commuter Express ACE, (http://www.acerail.com/), is an Amtrak express train running from the central valley towns of Stockton, Tracy, Livermore and Pleasanton to San Jose. The train stops at the Santa Clara Amtrak station at Lafayette and Tasman, near the Santa Clara Convention Center 5099 Stars & Stripes, Santa Clara, CA 95054. Only a few trains run per day. Note that the Santa Clara stop doesn't include a station building, just a platform under an overpass, so plan connecting transportation before you arrive.
Amtrak California's Capitol Corridor train runs between Sacramento and San Jose via East Bay cities such as Berkeley and Emeryville. The Santa Clara stop is the same as the ACE above, with no building. The nearby Diridon station in San Jose is better equipped and includes a building with a ticket counter. It may even be closer to parts of Santa Clara. Read schedules carefully, since some trains include a bus connection.