By ship
The easiest way to get into Thonburi is by boat. The Chao Phraya Express Boat goes up and down the river for 15 baht. Sometimes cashiers want you to buy the ticket before embarking the boat, but it is allowed to buy tickets inside. If going north from Sathorn pier from Silom, the first pier on the Thonburi side is Wang Lang. It's the easiest point of entry as all lines stop there and the Wang Lang area is one of the more interesting ones in Thonburi. If you're heading south from Phra Arthit pier from Khao San Road, Wang Lang is the second pier on the Thonburi side. When you're heading for the Royal Barge National Museum, disembark at the Phra Pin Klao Bridge pier.
There are also numerous ferries crossing the river from the Rattanakosin and Silom sides. Many Bangkok commuters make use of these ferries, as they quickly cross the river for only 3 baht. If you're visiting Wat Arun, head for Tha Tien pier at the Rattanakosin side and embark take the Wat Arun ferry service. Other notable ferry services are from Tha Chang to Wang Lang and from Tha Phra Chan to Wang Lang.
By Public Transit
Most travellers will visit Thonburi as a day-trip from Khao San Road, Sukhumvit or Silom. After nearly ten years of delays, the BTS Skytrain connection to Thonburi finally opened in May 2009. The only two stations on the Thonburi side Wongwian Yai and Krung Thonburi aren't near anything particularly interesting though. The best way to get into Thonburi is by getting off the Skytrain at Saphan Taksin station, near the end of the Silom Line, and taking the Chao Phraya Express Boat up the river.
By bus
Getting into Thonburi by bus is very complicated, so only use city buses as a last resort. Bus travel is necessary to reach some destinations though, such as the Taling Chan Floating Market. If heading there, take ordinary and air-conditioned bus 79 from Ratchadamnoen Klang Road, which is near Khao San Road. Make sure you take the bus into the right direction crossing the river and ask local passengers when to get off or you might get lost.