By train
Trains leave Bangkok's Thonburi Train Station at 07:45 and arrive at Kanchanaburi at 10:20, also at 13:45 and arriving at 16:35. You may be interested in buying a ticket all the way to the River Kwai Bridge, since these two trains are the only ones which cross the bridge each day. Since December 2005, the fare is 100 baht for foreigners.
Be warned that reaching Thonburi Station from Khao San Road is harder than it looks; tuk-tuk drivers will try to charge you outrageous rates, and walking involves crossing two bridges and looping back a ways. The best way is probably to take the passenger boat from Phra Arthit Pier and connect to a cross-river ferry that reaches the Thonburi Railway pier, then walk or take the open minibus from there. You can also walk a bit away from Khao San Road and find a metered taxi that will not rip you off. The fare should be about 70 or 80 baht from Khao San on the meter.
Return trains leave at 07:25 and 14:48 from the main railway station; from the River Kwai Bridge they leave 6 minutes earlier. Riding 3rd class is an adventure in itself, and definitely recommended.
Both train services continue to/from Nam Tok, the current terminus of the Death Railway. The normal trains will charge "Farangs" Westerners B100 in each direction from Kanchanaburi to Wang Pho, the last station before Nam Tok as at late 2009Thais pay a lot less.
The 10:30 train has a special tourist section, where the low, low price of 300 baht gets you air-con, a soft drink and a certificate of having ridden the Death Railway. This service has occasionally been operated by a steam engine, but usually uses an ordinary diesel DMU, and railfans will have to content themselves with the Japanese-era steamers plinthed at the main and bridge stations, also at the waterfall in Nam Tok Noi. As at late 2009 the steam train rides no longer operate.
By bus
BKS public buses line 81 leave from Bangkok's Southern Bus Terminal Sai Tai Taling Chan สายà¹à¸à¹à¸à¸¥à¸´à¹à¸à¸à¸±à¸, which is located far west in the suburb Thonburi. In Kanchanaburi, there are two separate but nearby bus terminals, with 1st class buses departing from an office off Thanon Saengchuto, and 2nd class buses from the larger terminal one block east.
1st class buses should leave Bangkok every 15 minutes from 05:00-22:30, take about 2 hours, and cost 110 baht, including a bottle of water.
2nd class buses new route leave Bangkok every 20 minutes from 03:30-19:00 and take about 2 hours. Cost 95 Baht.
2nd class buses old route leave Bangkok every 15-30 minutes from 04:00-18:00 and take about 3 hours.
There are also tourist minibuses directly to/from Khao San Road, departing Kanchanaburi at 13:30 and 18:30.
There are also some buses leaving less frequently from Bangkok's Northern Mo Chit bus terminal note: not the same as Mo Chit BTS station, and not within walking distance of it, although a standard 50B moto ride is available. It's often called "Mo Chit 2". Here are the times I could find at the station:
First-class bus with toilet 3 hours, 122 Baht06:00, 11:00 14:30
Second class bus with no toilet inside not sure about time and price, time is probably the same05:00, 07:00 09:30 12:30 17:00
Bus rides may be variable or cancelled for example, with 14:30 being last of the day. BUT there are vans available at the bus station leaving even when you're told there's no way to get there by bus! It may pay to talk to the information desk for this. Price Feb '11 was around 120B, about 2 hrs.
From Nakhon Pathom, there are direct buses 2nd class only every 15 to 30 minutes between 04:00 and 18:00, which take two hours. Alternatively, you can hop off a 1st class bus when it passes by Nakhon Pathom, but double-check with staff to ensure the route allows this and they know your plans.
From Sangkhlaburi to Kanchanaburi, you're spoilt for choice:
Air-con VIP buses leave at 08:45, 10:45 and 14:30 and take 4 hours.
Air-con minibuses leave at 06:30, 07:30, 11:30, 13:00, 15:30 and take 3.5 hours.
Standard buses leave at 06:45, 08:15, 10:15, 13:15 and take 5 hours.
By car
Kanchanaburi is about 3 hours drive from Bangkok, along the highway no.4 Phet Kasemfrom Bangkok until it hooks up with Highway 323,this will take you all the way to Kanchanaburi.
You can catch a taxi to Kanchanaburi, return to Bangkok for the day for around 2,000 baht. This should include stopping at the Bridge over River Kwai and museum, Kanchanaburi township, the local dam and the cemetary for the prisoners of war. You may need to pay a bit extra to visit Erawan Falls which is about an hour out of the town centre and the Tiger Temple.