By air is how most visitors arrive. Dublin Airport (DUB) is by far the largest hub, with direct flights from North America (New York, Boston, Chicago, Los Angeles, and others), most European capitals, and many regional UK airports. Aer Lingus and Ryanair are the main carriers, though transatlantic routes are also served by United, American, Delta, and Air Canada. Cork Airport (ORK) and Shannon Airport (SNN) receive some international flights, including transatlantic services to Shannon from New York and Boston.
From within Europe, flights to Dublin take 1–2 hours from most destinations. Ryanair in particular serves a large number of secondary European airports at low cost, though factor in baggage fees and the journey from Dublin Airport to the city centre (about 45 minutes by bus).
By ferry is a slower but often enjoyable alternative, especially if you are bringing a car. Stena Line and Irish Ferries operate crossings from Holyhead (North Wales) to Dublin Port, taking around 2–3.5 hours by fast ferry or just over 3 hours on the standard service. Pembroke to Rosslare (County Wexford) is another option, taking about 4 hours. From France, Brittany Ferries runs a Cork–Roscoff service (taking around 14 hours) and an Irish Ferries service connects Cherbourg with Dublin (about 19 hours). Ferry crossings can be scenic and much less stressful than airports if you book in advance and avoid the peak summer rush.
EU citizens need only a national ID card to enter the Republic of Ireland. Most other nationalities need a passport. Ireland is not part of the Schengen Area, so a Schengen visa does not cover Ireland — check visa requirements for your nationality before traveling. Citizens of the US, Canada, Australia, and New Zealand can stay for up to 90 days without a visa.
Note that Northern Ireland is a separate jurisdiction (part of the UK), and crossing the border between the Republic and the North is seamless — there are no checks — but be aware that different rules apply on the UK side.