yeah, coming from someone who has had to do this any number of times (usually to redwood city, not palo alto, but still same direction)..... it is a huge pain in the butt.

it usually takes me around 2 hours all told to use the caltrain, whereas if someone picks me up in a car, it takes about 20 minutes terminal to doorway of house.

seriously, someone dropped the ball here. california does a much better job than many other us locations at public transit, but if you want to head south from sfo, you are pretty much up the creek.

rt1flea is correct:
from the airport, you take the BART NORTH to San Bruno. get off.
next, take the BART SOUTH to Millbrae. get off.
now, take the Caltrain SOUTH to..Palo Alto. get off. walk 1 mile onto campus.

and your day is shot.
for me, it was 3 different trains, 2 tickets, and a lot of time, all within essentially one travel zone. and someone was always hogging the machine, you would sit there all antsy waiting to get a ticket as the train rolls in, and if you ARE in a hurry and decide to jump the train without paying, you a.) feel like a bad person and b.) are in serious danger of getting a huge fine and getting kicked off.

samtrans may be the way to go. haven't tried it.