Ferries leave from Trapani to the Egadi Islands regularly they mostly travel to Favignana, Levanzo and back to Trapani. The ferry to Marettimo is less often. Look into current prices and travel info at these web sites.
Hydrofoils are more expensive than the slower ferries that take cars but they run more frequently.
I usually arrive by bus and then deal with what ferry is the best option from then on….don’t plan anything….. your in Sicily. Relax…. if it is going to be a while, go for a walk or have lunch.
Ok this is a quick and easy tip. While the train system thru most of Italy is great (Or Fantastic by Australian standards) the train line from Palermo to Trapani is not. After telling someone this and having her ignore me I had the added frustration of waiting for her at the end of the line. Take a bus, they run more often and are more reliable.
AST bus lines
Transport timetables for Sicily
The most fun way to get around Favignana is by scooter. A must do! You'll be able to really see the island, and explore the calas, see amazing views, little beaches. . .