You'll qualify for visa free travel if you meet the relevant criteria, which basically means holding machine-readable or electronically chipped British passports (or passports from another country included in the US Visa Waiver Program)
http://www.usembassy.org.uk/cons_new/visa/niv/ mrp_bio.html
and you've never been arrested or convicted of any offence:
http://www.usembassy.org.uk/cons_new/visa/niv/ vwp3.html
(Anyone who doesn't meet that condition is obliged to go through a lengthy visa application process, which usually takes several months).
The USA normally insists upon visitors having 6 months validity on their passports but that condition is waived for British passport holders. You passports just need to be valid throughout the duration of your stay.
If you qualify for visa-free travel,you're required to make ESTA (= Electronic System for Travel Authorization) applications online at least 2 days prior to travel:
http://www.usembassy.org.uk/cons_new/visa/niv/ esta.html
Chris