Took me a while to find it myself.
Since 12 January 2009, UK travellers to the US under the Visa Waiver Programme (VWP), which allows most British Citizen passport holders to visit for up to 90 days without a visa, have required an authorisation via the Electronic System for Travel Authorisation (ESTA) prior to boarding a carrier to travel by air or sea to the US. Travellers can register for authorisation online through the ESTA website at https://esta.cbp.dhs.gov
and are advised to do so at least 72 hours prior to travel. See the Entry Requirements section for more details.
Basically, you'll need to go online to the address in the quote and register your details there. Make sure you get a copy of the number they give you - print the page and keep it with your documents is best.
You'll still need to fill out a Visa Waiver form and Customs form that they'll give you on the plane and you need to get through Immigration.
They'll staple the Visa Waiver into your passport - DON'T lose it! And make sure they remove it on your outward trip as, in theory it can cause all sorts of problems.
If you have to make a connecting flight when you get to the US, make sure you leave yourself plenty of time as going through Immigration and Customs can take quite some time. I speak from experience here.
Hope that helps - if you need any more advice, let me know here and I'll try and help.
Wyrd bið ful āræd.
"Coffee. The finest organic suspension ever devised. I beat the Borg with it."
- Capt. Kathryn Janeway