To create an Itinerary use the handy trip planner at 511.org
East Bay: Take BART all the way to Fremont. Make sure to get a transfer on your way out in Fremont! Once outside, look for Santa Clara VTA Route 180. The bus runs every 15 minutes midday but check the schedule at www.511.org yourself to make sure. Take this bus to the Civic Center Light Rail station at the corner of First and Mission in San Jose. The fare for the light rail is another few dollars, as VTA does not do transfers!
Next, take the light rail north (back the way you came) from the Civic Center station to the Metro/Airport station. You can, if you like, walk from here; it’s about a ten-minute walk. Just walk down Metro Drive (the street the light rail crosses) to Technology Drive, turn right on Technology, cross Airport, and the Doubletree will be just on the other side of Airport on the right.
If you have mobility issues (‘my luggage is full of ritual garb’ counts!), you can catch the VTA 10 at the Metro/Airport light rail station. This bus might be free but be ready for another few dollars just in case. It runs every 15 minutes at peak and stops at the corner of Airport and Gateway where the Doubletree is. (verified on www.511.org)
San Francisco and the Peninsula: Take Caltrain to the Santa Clara station. Fare for this leg will be variable based on distance traveled. The trains run approximately every 30-60 minutes. From Santa Clara take the VTA 10 bus past the airport. It will drop you off at Airport and Technology right across the street from the Doubletree.