Shuttle vans run from the airport to various locations in the city door to door. Most of them have a desk in the baggage hall and on the arrivals level. About taxis, it is recommended to agree a price with the driver before using the taxi (a common fare between the airport and the Vitacura area is around 14000-16000 CLP, US$30.00 - 35.00)
In order to travel by Metro and buses in Santiago, you must have the BIP card (tarjeta BIP) that can be acquired in the Metro stations.The cost of the card will be CLP$1250 and you may load it with at least $1000 more which will cover at least two trips that do not take more than 90 minutes in total.
If you continue to Viña del Mar by public transportation, you may take a bus to Metro station "Pajaritos" from where buses to Viña del Mar leave every 30 min. A good choice are the Centropuerto buses that leave the airport every 10 minutes, from 6:40 until 23:30 hr. The cost of a one way ticket until the metro station "Pajaritos" is CLP1400 (around US$3.00). On arrival to Pajaritos, just go to any bus office (Tur Bus, Condor Bus, Pullman Bus, etc), buy a ticket to Viña del Mar and get off at the bus terminal there. This map shows the distance from the bus terminal to the Hotel San Martín.
