Erice is about 90 km (one and a half hours' drive) from Palermo Airport "Punta Raisi".
The transport from Palermo Airport to Erice on June 9 and back on June 19, is arranged by the Centre and included in the course fee. Transport on other days is not included in the course fee, but the Centre can arrange it if requested. An estimated price of one way transport is 50 Euro.
Similarly, the transport from/to Airport "San Vinzenzo Florio" in Trapani-Virgi, Trapani Railway Station and Trapani Port Harbor (on June 9 and 19 only) is arranged by the Centre and included in the course fee. Transport on other days is not included in the course fee, but the Centre can arrange it if requested.
You have to take the Trinacria Express from Punta Raisi to Piraine and then a connection to Trapani. The time needed is from 1h 42 min to 4h 11 min if you leave Punta Raisi at 5.55 am. The cost should be under 10 Euro.
The cheapest connection to Trapani from Palermo airport seems to be by bus and it costs 6,80 Euro. But there are only three rides from the airport on 12.30 (not on Sunday and holidays) 18.00, and 22.30. Timetables can be found here.
Funivia (cable car) Trapani/Erice operates on weekdays from 7.40 to 20.30, on Saturdays from 9.30 to 24.00, and on Sundays from 9.30 to 22.00. The price 2.70 euro (return ticket 5 euro).
A bus from Trapani to Erice takes less than one hour and costs less than 2 euro. On weekdays (Monday-Saturday), there are 7 buses daily that depart Trapani at 6:40, 8:30, 9:30, 11:30, 14:00, 15:30 and 17:30. On Sundays and Holidays there are 4 additional buses at 9:00, 11:00, 15:00 and 17:00. Trapani-Erice bus timetable can be found here.
Unfortunately, there is no direct public transportation to Erice. Whether you are travelling from Palermo Airport or Trapani Airport, you will need to go through Trapani to get to Erice. However, the Center can arrange direct transportation by taxi at additional cost (on days other than June 9 and 19).
From Palermo, take the highway A29 (E90) direction Trapani Birgi for 65Km, continue along A29DIR (E933) for about 37km, then along SS187 towards Valderice where you turn left and take Via Erice that will lead you to Erice by SP31 (about 5km).
Palermo Airport is about 35 km far from Palermo. There is the Trinacria Express to and from Palermo (which costs 5 Euro). Timetables can be found here.