There are an increasing number of direct flight options from the UK, Ireland, USA & mainland Europe to one of Sicily's three international airports in Palermo, Catania & Trapani.
If you're visiting Sicily as part of an Italian driving holiday, then one of the regular ferries from Reggio Calabria to Messina are very convenient.
If flying isn't your thing, or it is more practical for you to catch the ferry to Sicily then several options exist.
There are also good rail links to Sicily from the Italian mainland. Incredibly these trains are actually loaded onto a ferry at Messina for the short boat ride to Calabria.