If you want to do everything strictly in accordance with the rules which are stated on website of the US embassy,
you're meant to apply for a visa. (According to the website, anyone who's ever been arrested, even if completely innocent, is ineligible to use the Visa Waiver Program).
However, that process is incredibly long-winded (taking up to 6 months or more), time consuming (you have to attend an interview in London) and expensive (you have to pay an application fee, plus a further fee for a courier to return your passport, as well as the money to travel to the interview).
More importantly,
the visa application process would be completely pointless anyway. There are two reasons for this:
Firstly, part of the process involves submitting a copy of your 'police record' to the US embassy. Since that record is blank, they'll just be confused as to why you're applying for a visa, rather than using the waiver program.
Secondly, the US immigration authorities have no direct access to UK criminal records (even when they actually exist). They've only got a list of high-risk individuals (such as suspected terrorists or drug-traffickers) provided by the UK authorities. So there's absolutely no way that they could know about your brush with the law.
Just use the Visa Waiver Program (while 'forgetting' about your arrest); you'll have no problems.
As you're probably aware, you now have to apply online, at least 72 hours prior to travel. Information (and the link to the online form) can be found here:
http://www.usembassy.org.uk/cons_new/visa/niv/ esta.html
Chris