If you are British, to qualify for the visa waiver programme, you must (with effect from 26th October 2004) have a machine-readable passport (with a bar-code at the bottom of the photo page).
This is taken from the web site of the Foreign & Commonwealth Office:
"The US operates a Visa Waiver Programme (VWP), available to most British Citizen passport holders travelling on business, pleasure or transit from where they normally reside and who intend to stay in the US for less than 90 days. The VWP is not available to other categories of British nationals and you should check the data/photograph page of your passport to see whether you are described as a British Citizen. If you are not, you should consult the information on the Visa Waiver Programme on the US Embassy website (details below) for further information.
From 26 October 2004, all British passport holders, including children, travelling to the USA under the VWP will need their own machine-readable passports (MRP). From 26 October 2004, anyone without a MRP, including children who are currently on a parent's passport, will need a visa to travel to the USA. See paragraph below on UK passports to find out if you hold a MRP."
If you qualify for this, all you need to do is complete the forms which you will be given on the plane.