The old centre is compact — you can walk from Trinity College to Dublin Castle in ten minutes. Most major sights are within a 30-minute walk of each other. Walking is almost always the best option for the historic core.
Buses cover the wider city, operated by Dublin Bus. The network is extensive but can be slow in traffic; the Leap Card (a reloadable smart card) is the most convenient way to pay. Luas trams run on two cross-city lines connecting the Docklands, the city centre, and suburbs to the southwest. The DART (Dublin Area Rapid Transit) is the suburban rail line running along the coast from Malahide in the north to Greystones in the south — invaluable for reaching Howth, Dún Laoghaire, Dalkey, and Sandycove.
Taxis are plentiful and can be booked via the Free Now app. Cycling is possible but the city is not particularly cycle-friendly in the centre. Dublinbikes, the city's public bike scheme, has stands across the inner city and is cheap for short journeys.