As Jainey states, UK passport holders 'of good character' can enter the USA under the Visa Waiver Program. (You just fill in a form).
However, if you've ever been arrested (even if you were completely innocent of any offence) you cease to be eligible for the VWP and you must apply for a visa. The process takes about 5 to 6 months and details are in my posts here: http://www.theanswerbank.co.uk/Travel/Question 289769.htm