We've heard there is service from the Naples/Sorrento area to Sicily on both train or ferry. Hard to find. Does someone have experience doing this?
For trains you need to check Trenitalia. Napoli and Reggio Calabria are separated by merely 4h30 by train (the faster ones). From there you can cross the strait by ferry and continue your trip from Messina to Catania (+1h40) and Palermo (+2h), on top of roughly one hour to cross the strait and any waiting time. There are also overnight ferries between Sicilia (Palermo and Catania) and Napoli/Salerno. But they are usually an expensive proposition for the cheap cabins you get.
www.ocean24.com, hit English flag and then zoom into the map e.g. to Sicily. Then click on any of the flagged ports to see the routes served to/from there. You can book right on that website. It'd part of Dertour, one of the largest, Germany-based pan-European tour operators.