The easiest way is to rent a car at the airport.
(for example www.sunnycars.com or www.mytripcar.com)
By Bus
Regular busses are leaving from Alicante and Valencia airport (to Denia and Ondara)
check www.alsa.es
By Taxi
Coming with more people, a taxi might be an idea
check www.facebook.com/Roadrunnerscostablanca (praten Nederlands), www.taxialicante.eu or www.beniconnect.com