Capers are big business on Pantelleria. Personally I hate eating them, though I'd happily add them to salads and sauces when cooking for others.
We went to the place where it all happens on the island... a Co-op in a really out of the way place near Scauri. It is not much more than a shack. The factory was opening the week we were leaving so we didn't get to see much action. Essentially the co-op collects all the harvest from small farmers around the island, packages them and then sells them to the mainland or overseas. The guy behind the counter proudly told us that they could do internet orders as well.
Alternatively, you can find capers in any of the shops in Pantelleria town... or even back on the mainland really. Though there's nothing quite like getting them right where they were born.
What to buy: The zibibbo is a famous wine from Pantelleria. It is sweetish... and the locals here drink gallons of it. At the hotel where we stayed there was a free flow of zibibbo during meals, which was a lot of fun.