Take a public taxi from ground floor G8 at the International airport to downtown or any of the river hotels, shouldn’t be any more than £35.
For local short runs take a tuk tuk which is like sitting on the back of a wasp racing to sting somebody…its fun and cheap. Make sure you make it clear that you want to go straight to your destination and not via a gem or silk store. Most trips are about 2/300 baht or less.Pink taxis are relatively expensive same trip would cost 700 baht.
On the water a private long boat can be hired for about an hour at £35, these will take you along the klongs (canals) to catch a glimpse of a quieter Bangkok life.
But if you merely need to move up the Chao Prayor river a public ferry for several stops is 20 baht….from these stops you can easily see Chinatown, the Golden Temple and Wat Arun.
Didn’t use the train system but this also links to the river and airport.
For more about Bangkok and Thailand, click on the links below.