Use the river ferry to get around, it's quick, frequent and cheap.
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There are different boat lines on Chao Phraya river and also boat lines into the klongs. A good description on how to use can be found here: traveltobangkok.blogspot.com/search/label/Bangkok%20by%20boat%20-%20Chao%20Phraya%20River%20and%20Klongs
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