Getting to and departing from Bangkok is convenience via 2 international airports: the new Suvarnabhumi International Airport, about 30 km east of central Bangkok; and the old Don Muang Airport in the north. Both airports are well connected to the city center: From Suvarnabhumi International Airport is accessible via the Airport Link http://www.srtet.co.th/en/ or via regular taxi services. From Don Muang Airport is accessible via the taxi services.
Travelling around the city is easily by taking taxis with reasonable fare, or tuk-tuk, motorized tricycles taxi, which is usually bargained fare. However, the city center and most of the sightseeing can comfortably be reached by BTS skytrain (http://www.bts.co.th/customer/en/main.aspx) and MRT underground train (http://www.bangkokmetro.co.th/)
For more detailed information, please check http://wikitravel.org/en/Bangkok