Is there a fast train from Naples to Sicily?

which city in Sicily are you going to?

I'm not aware of any so called 'fast' train. Train from Naples is about 6-10 hours depending on where in Sicily you're going. Only fast option is flying.

Would like to go to Taormina

You should be able search your options on
http://www.trenitalia.com/tcom-en

Okay, I was a little off on the train times, looks like it's more like 7 hours by train from Naples to Taormina. If you flew, you'd fly to Catania, then bus/train to Taormina. Neither option is quick or easy.

Having spent a large part of a day on a cramped , slow and crowded train from Lamezia Terme, south of Naples to Catania, I highly recommend flying. We took the train for the romance of train onto ferry and back onto land but it takes quite a bit of time to uncouple the train, move it onto the ferry and repeat. The rolling stock was quite old, very warm and crowded. The crossing itself was lovely as we left the rail car and stood on deck to observe all the boat traffic in the Straits of Messina in the sunshine. Wouldn’t do it again, too much time wasted when we could have been seeing more of Sicily.

Whatever you do, don't try to save time by taking the overnight train. Utterly miserable.

Sicily is fascinating and can keep most people occupied for over two weeks. I wouldn't go just to see Taormina. Too much travel time, not enough sightseeing time.

I loved Taormina. That said, I agree that it's probably not worth going to and from Naples for just a few days, if Taormina is the only place you're going in Sicily.

From Naples, you can fly to Catania or Palermo (several flights per day to each). If you have enough time, flying into one and out of the other, and seeing a chunk of Sicily, is great. If you have more than a few days but less than two weeks, you could certainly fly in and out of Catania and see eastern Sicilian destinations like Taormina, Catania, Siracusa, Noto, Ragusa, etc. Many of these have direct buses to the Catania airport.

If you have time, another option is the overnight ferry between Naples and Palermo, which is said to be nicer than the train (no personal experience).

Flying is the best but do not go to just one place while in Sicily. See everything west to east, u will not be disappointed. I was there last yr june. Had a fabulous time And saw alot.
U need 7-10 days, a great destination imo. A tour is a good idea if u can. Enjoy,

Make sure you go to Cefalu. beautiful seaside village