From Santorini Airport to your destination: Taxis (tel. 22860-22860 /22555) outside of the terminal charge a fixed price - a price table is posted inside.
The KTEL bus (tel. 22860-25404 /25812) stops outside ofthe terminal, departing to Fira every 15 minute & taking about 15 minutes; from there you can change to other buses serving different towns. Note that even though Santorini hotels offer shuttle service at a fee, the fee is usually higher than that of a taxi.