Board at Roma Termini, sleep through the ferry
Arrive at Roma Termini with time to find your carriage — there's no separate check-in, just your ticket and your berth number. Somewhere around Villa San Giovanni, in the middle of the night, your train will be shunted onto a ferry and carried across the Strait of Messina to Sicily. You're not required to be awake for it, though it's worth setting an alarm at least once to see it.