We got to Pantelleria from Trapani in Sicily by hydrofoil. The trip takes about 2 and a half hours and you need to buy your tickets in advance.
Sadly I thought it would have been more fun. It was highly uncomfortable and I felt a bit more than woozy, because the seas were quite choppy as well. You have to sit down at all times on a hydrofoil for safety reasons... something I didn't know before. Not exactly the leisurely boat ride I had expected.
Nonetheless, it was one of the quickest way to get there (ordinary ferries can take up to 6 hours) besides flying of course (which is what we'll do next time).
At the height of summer, everything becomes more expensive and this includes the price of renting a little scooter. At €50 per day, we thought it a bit excessive but there you go.
Neither my husband nor I had ever had to drive a scooter before (pillion didn't count), so it was an adventure just getting started. In Italy you're fine to drive one of these small ones with a normal drivers licence.
To get round the island, you need less than €5 worth of petrol... so don't be like us and insist on a full tank (abt €10). The scooters come empty-tanked, so we were speculating that the rental agencies syphon out excess fuel daily from the dozens of stupid tourists who fill 'em up.
Scooters were a great way to see the island, but at times nearly impossible due to the heat. So you might want to consider renting a small car for the day as an alternative.
You get there either by plane from Palermo or by boat from Trapani (about four hours). When arriving by boat, you come into the port where the town of Pantelleria is located.