From 12 January 2009 it will be compulsory for non-US citizens travelling (to the United States of America) under the Visa Waiver Programme (VWP) to apply via the Electronic System for Travel Authorisation (ESTA) no later than 72 hours prior to departure.
Each approved ESTA will be valid for two years from the date of authorization, or until their passport expires, whichever comes first. However, for each subsequent visit within that period, details including departure city, address while in the USA, airline and flight number will require updating again.
The ESTA website is https://esta.cbp.dhs.gov/esta/esta.html
This web site is free. It is a service run by the US government which will replace those green forms you used to have to fill in on the plane.
If you do a search on the internet, you will find loads of dodgy web sites offering to do this for you, they typically charge between $50 and $250. This service is a con.
The basic package they offer provides you with documentation on how to fill in the form. All the documentation is freely available online from the link above.
The executive service will fill in the forms for you. The questions are simple and answers are obvious. For example “What is your name?", “Have you ever been or are you now involved in espionage or sabotage; or in terrorist activities; or genocide?” - Yes or No, “Are you seeking entry to engage in criminal or immoral activities?” - Yes or No. If you need help with these questions maybe you
should pay for their service!!!
Some extra help can be found here:
British Airways US Immigration requirements
Wikipedia - Visa_Waiver_Program
Department of Homeland Security - Frequently Asked Questions about the Visa Waiver Program (VWP)
As an extra note from the 8th September 2010 the US Department of Homeland Security (DHS) will be introducing an administration charge of $14 when applying for an ESTA.