To reach Galway, you will have first have to take a flight to Dublin. As of now, there are no direct flights between India and Ireland and hence, you will have to take a connecting flight to Dublin first, and then take either a bus, train or flight depending on whichever fits your schedule. Flights to Dublin are provided by carriers like British Airways, Swiss Air, Lufthansa and several others.
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.
Shannon Airport, located about 90 minutes away from Galway is the airport which serves western Ireland. Galway's airport has been closed since 2011 due to it's short runway. Shannon Airport has flights connecting it to Europe and North America.
The city is connected mainly by three national motorways, the M6 running east and west of the city, the M18 to the souther cities like Limerick and Cork, and the N17 with cities in the northwest.
Galway's main railway station is Ceantt Station, located in Eyre Square. Trains connecting Galway to Dublin, Limerick, and nearby cities.
The best way to get around Galway is by walking. Most of the places of interest are a maximum of 30 - 40 minutes away by foot. If you're looking for quicker options, you can take the bus or the taxis which run throughout the commercial areas of the town. Renting a car is not highly recommended since parking in the city is expensive.