During the summer, Pantelleria can be easily reached by regular flights from the main Italian airports (Roma, Milano, Venezia, Napoli, Palermo, Trapani, etc) or by ferry boat from Napoli and Trapani. Moreover, several low cost flights are available from July directly from several European airports.
There is some good advice at ‘The Thinking Traveller’ website.
To search for flights, try SkyScanner
From Palermo and Trapani the flights to Pantelleria can be found onwww.mistralair.it