Sicily getting from Palermo to Messina

Try rome2rio.com for these sorts of questions. It gives you various transportation options, along with time and approx. cost.

You can take the regionale train. It's inexpensive, and reliable. It's the entire distance of the north coast from East to West, and will take several hours. I took the train from Taormina through Messina to Cefalu. Spent a few days in Cefalu, and from Cefalu to Palermo. Very easy. You don't have to buy in advance, just go to Palermo's main train station, buy a ticket and go.