Soulopoulos,
Welcome to California in advance. You will most likely be flying into SFO and not SJC if you're coming from Europe. You will be arriving in the SF Bay Area, where public transportation is not particularly good. Here are your options for getting to the Hyatt:
(1) Download the Uber or Lyft app (iphones and androids) and request a car to pick you. You can use that service to get around the local area affordably. It is more reliable, more enjoyable (way nicer cars!), and cheaper than taxis.
(2) You can rent a car at SFO. This is pretty easy to do with tons of companies at the airport you can choose from (Enterprise, Herz, Dollar, etc.). You have the advantage of having your own vehicle to get around as you choose, but you will will have to drive in a foreign country. I know what that feels like and it's not always preferred on an international vacation. If you're renting for a couple days, the cost will probably be similar to using Uber or Lyft. You will simply return the car to SFO before you leave.
(3) If you insist on public transportation, you can just use Google Maps and it will tell you how! But basically, you would take BART from SFO to Millbrae. From there, you would take Caltrain southbound into Santa Clara/San Jose. From there, you will take the VTA light rail that Doug described above. This will be your most inefficient route ... it will take you 2-3 hours vs. a car ride which will be 35-45 minutes without traffic. Good luck!
- K
yes I'll pick u up and you can drive us back. Won't be as fun as last year if I didn't have my co pilot wanting to gun on ramps. 
