Caltrain will probably get you between the two in somewhere between 45 minutes and an hour on a weekdays. Weekends, you're screwed. Trains run once an hour at the best of times, and are basically broken all weekend due to maintenance for the foreseeable future. (I think they're using buses to connect gaps in service on the weekends).
Palo Alto is a (mostly) wealthy suburban town next to Stanford U. Without traffic it is 30-40 minutes from SF -- twice as long when traffic is bad. There's a train that is lame by European standards but fairly good for the US, which takes around an hour, sometimes as little as 48 minutes.