You can easily get into Dublin by air via it's international airport. Trains from nearby cities run on a daily basis directly to Heuston Station and Connolly station, it's two primary railway stations. Many of the country's highways also lead into Dublin if you're coming via car, and it's also connected to Wales and England via waterways.
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.
Since Ireland is not part of the Schengen Visa area of Europe, a separate visa has to be applied for, for travelling to the country. Online application form has to be filled on the website of the Irish Naturalisation and Immigration Service, after which you will be taken to the VFS Global website to complete the payment and other requirements. The website will guide you through all the required steps in order for you to obtain your Irish visa.
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.
Commuting options in Dublin are aplenty. The most popular of which is the DART, the Dublin Area Rapid Transit connecting a large part of the city. The tram system, called Luas, is also widely used. It has two route lines. However, the oldest and till date the most used mode of transport in the city is the state owned bus system. Exact bus fare is accepted, and change tickets are issued if the passengers overpay, which are redeemed at the Dublin Bus Office. Daily passes such as the Leap Card can be used on the DART, the bus, and the Luas as well.