You have been correctly informed that a visa is required if you've ever been arrested (even if you were totally innocent):
http://london.usembassy.gov/add_req.html
However the US immigration authorities have no direct access to UK police records so, if you choose to 'forget' your arrests, (and travel with an ESTA under the Visa Waiver Program) the chances of you encountering any problems are virtually zero. The US authorities have to make a specific request in order to receive information about any particular individual. (Even so, you can't assume that the police have no record of your arrests. A standard CRB check wouldn't show them, and an enhanced check would only have shown them if they were deemed relevant to your employment application by a senior police officer).
If you're a British Asian the US authorities might well decide to check up on you, and seek information from the UK authorities. Otherwise (unless you have the misfortune to share the name of a known terrorist) it's probably unlikely that they'd do so.
If you decide to 'go by the book' and apply for a visa, follow the links from the left hand side of my link for the relevant information. You'll have to apply to your local police force for a copy of your 'police record' - even if it's totally clear - and pay the relevant fee. You'll also have to book an interview at the US Embassy in London. (The waiting list is currently 18 days). The processing time after that is around 5 days (unless you were, for example, arrested for possible links to terrorist organisations, or other serious crime - in which case the processing time could be over a year). You'll also have to pay for the visa application and for having your passport sent back to you.
If you decide to 'forget' your arrests, and apply for an ESTA, start here:
http://www.cbp.gov/xp.../travel/id_visa/esta/
Chris