What's quickest will depend on exactly when you want to leave, but as a rough idea BART + CalTrain is likely to be simplest (even if bus/buses might be faster depending on your exact arrival time)
For the CalTrain down to Mountain View, you have a few trains an hour in the week (more in peak hours). Most of these stop at Millbrae, a few stop at San Bruno. The CalTrain timetable page has the details, and lets you download PDFs for offline checking. I'd suggest you save the appropriate one.
To get to the CalTrain, you'll want to take the BART. Most likely you'd want to go to Millbrae, but the BART only goes there directly from the airport on evenings and weekends. In the day on a weekday, the BART will take you to San Bruno, where depending on CalTrain timings you'll either way for a CalTrain, or ride the other BART line down to Millbrae to pick it up there. (It's one stop from the Airport to either Millbrae or San Bruno)
You might find a bus quicker, but it likely won't always be, and I'd guess it'll vary much more.
So, I'd suggest you download the CalTrain timetable PDFs, then head to the BART station at the airport. Look at where trains are running to at that point, then compare that to the timetable PDF, and head to either San Bruno or Millbrae (maybe via San Bruno + change). You should be able to buy your tickets for both of these without needing coins - BART ticket machines take notes and some also take cards and CalTrain ticket machines take notes and cards
Alternately, use the SFO Free Wifi once you're through customs, and ask google maps for the best thing for that minute.