Etna is situated not far from Catania. The only way to get there by public transport is by buses AST. In Catania the bus leaves from piazza Papa Giovanni XXIII that is situated near the central train station of Catania. The bus leaves at 8.15. From Etna the bus leaves at 16.30. The average journey time is one hour and a half. The price for one way ticket is 5 EUR.
You can check teh timetable and bsu stops here (2016): Catania – Etna
You can also take a taxi, but it is rather expensive: one way trip 100 EUR.