The Palermo Airport, called "Falcone e Borsellino", is located in the "Punta Raisi" area, ~30 km West from Downtown.
Train: Take the train "REG21314 Palermo Centrale" and stop at the Palazzo Reale Orleans Station; the Church "SS Elena and Costantino" is very near.
Bus Shuttle: The bus shuttle ("Prestia e Comande" Company) will bring you from the Palermo Airport to Downtown (or viceversa). The journey is nominally 40 minutes, but it can depend on traffic. The ticket cost is 6,30 euros and you can buy it directly online. At the Airport, the bus shuttle terminal is located just outside the "Arrival" zone. There are more than 20 daily trips, at a frequency of 30 minutes, from 6:30 a.m. to 11:30 p.m. approximately.
Taxi: The taxi fare from the Airport to Palermo Downtown (or viceversa) is ~ 45 euros during the day; the fare is higher in the night.