Shannon Airport in County Clare is a much closer option to Roscrea than Dublin but either can be used. JJ Kavanagh offers direct buses from both airports to Roscrea.
To get into the Irish feel before you even arrive, fly with Aer Lingus (our national airline) or Ryanair.
Ferries are also an option if you want to bring your own car. Irish Ferries, Stena Line, P&O Irish Sea and Brittany Ferries operate a variety of routes to Britain and France.
Roscrea Train Station is a very old but charming building about 1km from the town centre. It is on Iarnród Éireann's Ballybrophy-Limerick line which is a commuter line. However, Dublin is easy to access as the trains to and from Ballybrophy are timed to coincide with Intercity services between Dublin and Cork. The trains have been improving immensely in recent years but it is still a fairly expensive way to travel outside of Dublin.
The cheaper and more efficient option is by bus. Roscrea is served by hourly buses between Dublin and Limerick (Bus Éireann Route 12) and by daily buses between Athlone (and occasionally Sligo) and Cork. (Bus Éireann Route 71/76)
Independent operator JJ Kavanagh runs services to Dublin and Shannon Airports, a good option if you want to get here without connecting in Dublin City Centre.
Buses are very reasonably priced and tickets can be booked cheaper online.
There are no local bus routes operating in the Roscrea area. However, the surrounding towns and villages (eg. Borris-in-Ossory, Nenagh, Moneygall, Toomevara, Mountrath, Birr, Templemore, Thurles) can all be accessed on Bus Éireann routes 12 and 71/76 which pass through the town.
Fares are much more reasonable than the train and buses bring you right into the centre of town, beside the castle (perfect for starting a day trip).