To get there from Bangkok, you can take the BKS public buses (line 81). The bus leaves from Bangkok’s Southern Bus Terminal.

When you get to the terminal, look for the stands 79 and 80 to buy your tickets.

I bought first class ticket for buses that leave Bangkok every 15 minutes from 05:00-22:30. It takes about two hours, and cost 110 baht including a bottle of water.

In Kanchanaburi, the bus drops you at the main terminal in the centre of the city.

From there, you can take a tuk tuk, or a taxi that will drive you to your guesthouse. If you do not have a guesthouse, gently ask the driver a recommendation based on your criteria and he should be able to find you something reasonable.