There are no direct flights from India to Dublin. That being said, indirect flights to Dublin are available from almost every international airport in India. Jet Airways, Etihad Airways, Lufthansa, Air France, Air India are a few of the airlines whose services you can expect to enjoy on your way to Dublin.
A huge number of flights fly into Dublin from all over the world. Aer Lingus is Ireland's flag carrier airline and Ryanair is the other Irish airline. Both are not very expensive and cover most of the major European cities. Other international airlines connect Dublin with the middle east and the Americas as well.
Getting to Dublin via car is not a very difficult task with several routes on offer. The M1 through to M9 all have routes leading right to the capital city.
Dublin has 2 main railway stations, with trains running to destinations such as Cork, Limerick in the west from Heuston station, and to Belfast and Sligo from Connolly station.
Dublin is accessed by various private bus companies such as GoBus and Citylink. Bus Eireann provides routes connecting most of the towns and cities of Ireland with Dublin.
There are primarily two routes over water to reach Ireland, from Liverpool in the England and Holyhead in Wales, among many other routes between the two countries. A ferry ticket to Dublin Port will cost you around EUR 38 or GBP 30 from most of the British ports.