By train is the obvious choice from Dublin. Irish Rail runs frequent services from Dublin Connolly to Maynooth on the western commuter line — the journey takes around 35 minutes and trains run every 20–30 minutes during the day, more frequently in peak hours. The station is a five-minute walk from the castle and the main street.
By bus, Dublin Bus route 66 connects Dublin city centre to Maynooth, stopping at various points including the university. The journey takes longer than the train — 50–70 minutes depending on traffic — and is mainly useful if you are travelling from a part of Dublin not well-served by the rail line.
By car from Dublin, Maynooth is about 25 km west via the M4 motorway. Take the Maynooth exit and follow signs to the town centre. Parking is available in the town but limited during university term time.
From Dublin Airport, the most straightforward route is to take a bus or taxi to Dublin city centre and then catch the train from Connolly, or to taxi/hire directly (roughly 35 km, about 40 minutes in normal traffic).