Dordrecht is well served by trains. From Amsterdam Centraal the direct intercity takes about an hour and ten minutes. From Rotterdam Centraal it is 15 to 20 minutes. The high-speed line passes through, and you can catch the Eurostar/Thalys to Brussels and Paris a short hop away in Rotterdam. International travellers usually fly into Amsterdam Schiphol; from there a direct train runs roughly every half hour and takes about 90 minutes.
By road, Dordrecht sits on the A16/E19 between Rotterdam and the Belgian border. There is parking on the southern edge of the old town at the P+R Energiehuis lot, with a short walk over the bridge to the centre. By boat, the waterbus from Rotterdam Erasmusbrug to Dordrecht is a slow but scenic 40-minute ride through the harbour and along the Oude Maas.