Welcome to FT!
Pullman (
www.pullman.cl) and TurBus (
www.turbus.com - site appears to be down right now) are intercity bus companies offering frequent, high-quality service between Santiago and Valparaiso/Viņa del Mar. They leave from the main bus terminal in Santiago. It's about a two hour trip from Santiago one way, depending on departure time.
You can get to the main bus terminal from the SCL airport by taxi or shared van service; check with the transportation desk just before the customs exit.
Enjoy your trip.