If you get on the slow boat from the far rough end of the harbour it costs 1 euro 50 cents for the hourly service to messina, it takes about 20 mins.
For Palermo you need to leave from another place on the train line.
The best way to get there is by car. No airports in this region.
Railway stations are most of time far away from town. Once we had to walk 15 km from town centre to the station. However, tickets are quite cheap.
I highly recommend to get around by car or even bicycle (warning: mountainous region!).