You can get to Abruzzo by air through Pescara airport, by one of numerous buses and trains leaving from all major Italian cities, and of course by car. Main destinations in Abruzzo may be: Pescara, Chieti, L'Aquila, Avezzano and Teramo.
Bus: Bus routes are connecting Rome and its airports, Naples and northern Italy with Abruzzo's major cities. You may take: Prontobus, Dicarlobus, Flixbus. Tickets are available online!
Train: Italian train system is very developed, convenient and easy to use. Check the route and timetable at Trenitalia website. Some of the routes (east-west direction) may not be the fastest, but for sure - most beautiful, with mountains, valleys and viaducts on your way.
Car: Abruzzo connected by the network of wonderful routes, including toll roads E55 (North-South) and E80 (East-West). Ride from Rome Fiumicino airport to L'Aquila or Avezzano takes about 2 hours, to Chieti and Pescara - about 3. Some time losses may happen at the GRA (Grande Raccordo Anulare) - orbital motorway that encircles Rome - due to heavy traffic. You can rent a car at any of Rome airport or City Rentals. Or get your car in Pescara, Chieti, Avezzano or L'aquila.