The easiest (and cheapest) way to get to Wat Arun is by boat, the boat will take about 15-20 minutes, this will save you time and money and will almost avoid any traffic jam.
1. Take BTS train and get off at Saphan Taksin station
2. Walk (about 1 min) to Central pier (or Sathorn pier) and take Chao Phraya Tourist Boat to No.8 Tha Tien pier
3. Get off at No.8 Tha Tien pier and take the Wat Arun tourist boat to the opposite side of the river where the temple is located (the fare is 3 Baht).
P/S: climbing to the top level of the pagoda is most highly recommended if you want to enjoy the beautiful river scenes of Bangkok.
PP/S: not sure how many have noticed that Wat Arun is actually the reverse design of Thai 10 Baht coins