Sardinia is the second biggest island in the Mediterranean Sea and can be reached within a few hours from any countries in Europe. There are no airports in Palau, you will have to fly to either Olbia airport a 30 minutes car journey to Palau or to Alghero which is two hours car journey. Here are the list of where to fly from, with whom and to where :

From the UK :
Easy jet and Meridiana fly to Olbia from London Gatwick and Bristol and Ryanair flies to Olbia from Birmingham and to Alghero from London Stansted, Dublin, East Midlands, Liverpool.
Jet2 flies to Olbia direct from Edinburgh, Manchester and Leeds/Bradford

From Holland :
Direct flights to Olbia with Transavia air

From Norway, Denmark & Sweden 
:
Direct flights to Olbia from Oslo, Stockholm and Copenhagen with low cost Norwegian air

From Italy :
You can check on Easyjet, AirItaly, Alpi Eagles or Volareweb for flights to Sardinia

From Germany & Austria :
Visit TUI, Easyjet, Ryanair, Skyeurope, AirBerlin 

From France and Switzerland :
Flights to Olbia with low cost companies like Easy jetMeridiana, TransaviaAirBerlin and to Alghero and Cagliari with Ryanair

From Belgium :
Low cost company Jetairfly from Bruxelles to Olbia

From Prague :
Skyeurope flies to Olbia

If you call or email in advance we can organise you a private transfer from the airports by minibus or taxi.
The most convenient way to visit Sardinia is to rent a car, at either airports you can find booking office or you can check the rental agent Sardinya who also have an office in Palau and airports, the rental agents Carhire3000, Hertz , Eurocar have offices in the airports of Sardinia.
There are bus services which are also available, you may want to directly for the bus timetable or you can contact the of Palau.