The nearest airport to Taormina is Catania Fontanarossa (70 Kms).  This airport, whilst small, is modern and newly built and is not nearly as chaotic as some Italian airports.  From Catania to Taormina takes under an hour to drive and costs from about 90 euros by taxi (confirm  the price ahead as they tend to overcharge you)  , 80 euros if you book it when you book your accommodation . 

By bus it takes around 90 minutes but costs only 5 euro (fewer busses in low season).

If arriving by train the nearest station is 'Taormina - Giadini Naxos' which is located on the coastal road. The recommended option is to take a taxi direct to the hotel. There is a taxi rank outside the station building and the usual cost is 15 Euro to the centre of Taormina. 

It is possible to hire a car and make the drive yourself - take the autostrada towards Messina and Taormina is very well signposted (out of the car park follow all of the green sign posts for A18, TANGENZIALE or AUTOSTRADE).  However Italian driving is generally fast and furious and drivers need to be very confident to cope.  Taormina itself is a challenge for even the most confident driver.  The majority of thestreets in the town are one way and many streets are very very narrow.  Unless you are driving a very small car you will probably drive with your wing mirrors in.  If you are planning on driving in Taormina it may well be worth parking up in one of the two large lots at the edge of town and walking your route first since the town isn't that big.  If you are travelling with a caravan or in a camper van don't bother unless you have nerves of steel and can cope with scraping the vehicle! All of the hystorical centre is pedestrian and there is no parking so you must use one of the two parking lots. Out of the motorway and tolls drive straight up to following the signs for the centre, once up the top you will find a huge concrete parking on your right hand directions to the centre on your left and a tunnel in front. To get to most of the hotels in town use the tunnel in front of you following the signs for castelmola it saves clutches and it is much easier.