By bus
BKS public buses lines 83 and 997 leave from Bangkok's Southern Bus Terminal. The trip costs 40 baht in first class and takes about an hour in good traffic. Buses go every 10 minutes from 4:10AM until 9:30PM.
There are also 2nd class buses to Kanchanaburi every 15-30 minutes.
In addition there is a non-stop minibus service between Bangkok's Victory Monument and the Big C Superstore in Nakhon Pathom. You can also ask to be dropped off directly in front of Phra Pathom Chedi. The Victory Monument is far more convenient than the Southern Bus Terminal, and is on the skytrain light rail system. But the departure point from Victory Monument is hard to find, being located under the expressway, about 50 metres north of the roundabout, on Phahon Yothin Road look up and around for the huge advertisement screen for the direction. At the other end, Big C is on the main road through Nakhon Pathom, and has plenty of four-wheel and two-wheel taxis to take you to your final destination. Cost is currently 60 baht each way.
By car
From Bangkok, driving on the old route of Petchakasem Road Highway No.4 passing Aom Noi, Aom Yai, Sam Phran to Nakhon Pathom or driving on a new route from Bangkok, passing Buddhamonthon, Nakhon Chaisi to Nakhon Pathom. The new route is Highway No. 338 and originates on Pinklao Road. The elevated part from Pin Klao Bridge to Buddhamonthon 2 Road is toll free and cuts down travel time considerably.