I went through this very recently (heading to Sunnyvale rather than Mountain View), and the only improvement I can offer for a first timer is to keep an eye out for Caltrain pamphlets that list all the schedules, fares, zones, and whether each train will be an express train or not.
Of course said pamphlet will not be available on the Caltrain platform, but I found one in a rack at the top of the staircase at Millbrae.
That pamphlet is called a schedule, it is posted in every station, and it is surprisingly readable and understandable. Only the larger stations have copies of the schedule to take, as well as on board every train. The only cryptic things are the train numbers, but you don't really need them, especially now that stations have real-time train arrival signs.
Of course said pamphlet will not be available on the Caltrain platform, but I found one in a rack at the top of the staircase at Millbrae.