Once at the Catania Airport (CTA), you have multiple options:

1. Alibus shuttle. Price: 4€. Time: 15′. === Best option ===
   Alibus allows you to get off at “Italia”, which is just less than 100mt far from the venue. This shuttle is suitable also for your way back to the airport. Timetable here. This shuttle runs from 4:40am until 00:30 every 30′. If you land between 00:30 and 4:40am, you need a taxi
2. Train. Price: 3.60€. Getting a shuttle to the train station of Catania Fontanarossa. Time: 15′. You may get off either at Catania Centrale or Catania Europa. You’ll have either 1.2km or 0.8km to walk. More info and tickets here
3. Taxi. Price: around 30€.

From your accommodation to Palazzo Scienze you may consider to get the underground (1€ per trip) getting off at “Italia”. From there you are just behind the venue.