The best way to reach Sardinia is by plane. Main airports in Sardinia are:
-Cagliari-Elmas Airport (10 km to downtown Cagliari)
-Olbia Airport (260 km to downtown Cagliari)
-Alghero Airport (240 km to downtown Cagliari)
From Elmas Airport there is a train service towards Cagliari, Piazza Matteotti.
The railway station is located outside the airport and can be reached easily by foot (please follow the indication signs at the airport).
The ticket (€ 1.30, one way) can be purchased from the ticket machines at the rail station.
Here you can see the timetable (from Cagliari-Elmas to Cagliari).
Bus Number 8 stops near Cittadella dei Musei.
From Piazza Matteotti you can take Bus Number 8 and get off at the first stop on Viale Buoncammino as shown in the map.
Then you can walk in the direction to Porta Cristina, pass Porta Cristina, and enter Cittadella dei Musei from the left.