If you are staying at a hotel or hostel in Viña del Mar, they can probably set up a taxi for you. If you have been staying in a private home, ask around to see if anyone has a contact. You could even pop into a small travel agency and ask.
If not, you could phone a couple of these for prices.
http://buscador.emol.com/amarillas/transportes+al+aeropuerto/viña+del+mar
www.rutaschile.com/men1/tourdetalles.php…
http://www.vivastreet.cl/traslados+vina-del-mar/transfer-aeropuerto-de-santiago--scl--desde-vina-del-mar/53371909
If that seems too expensive to you, you can take any Viña to Santiago bus and ask to get off at the "cruce del aeropuerto". There are always taxis waiting there to take passengers from the coast to the airport, only a few mins away.. But you may be nervous about this after dark.