The easiest parking garage with visitor parking is “Roble Field Garage” which google can tell you how to get to. It's a 5 minute walk from the garage to the Neurosciences building:
After 4PM on weekdays and anytime on weekends you can park in any areas marked A or C (except the oval, which is enforced until 6PM on weekdays) for free as enforcement times are only between 6AM and 4PM Monday-Friday. You can also find spaces in Parking Structure 1 (the area marked in purple in the map below) behind the Cantor Art Center. The parking structure has machines where you can pay by credit card for parking.
You can take Cal Train to Stanford → get off at the Palo Alto station and walk up Palm Drive to the oval and take a right down Jane Stanford Way and the Neurosciences building will be on your left. Note that Cal Train from the airport, well, sucks. You will likely have to take BART one station north, then switch trains to go one station to the south and then switch again to get a Cal Train that will take you to Palo Alto. Yes, this is the line that expects to become the Bay Area backbone of the futuristic bullet train system that, er, some other countries have had since the 1960's. Welcome to Silicon Valley - home of America's technology revolution. I recommend Lyft from the airport.