Anyone who's ever been arrested (even if totally innocent) is ineligible for the Visa Waiver Program. See here:
http://www.usembassy.org.uk/cons_new/visa/niv/ arrests_and_convictions.html
To enter the US legally, you must obtain a visa. You can fill in the application form online, here:
http://www.usembassy.org.uk/cons_new/visa/niv/ electronic.html
Then you need to schedule an interview at the US Embassy in London. See here:
http://www.usembassy.org.uk/cons_new/visa/niv/ interview.html
It typically takes two to three weeks to get an interview. The interview process takes two to three hours. Then, because you'll have answered 'yes' to the 'arrests and convictions' question, it will take a minimum of 14 to 16 weeks before you'll get your visa.
If you're invited to take part in the trial payment scheme, the visa application fee is US$100, payable by credit/debit card when you attend for interview. Otherwise, you'll be given a form, which you take from the embasy to a bank, to enable you to pay in �63.
OK, that's the 'official' answer out of the way. Now for the 'unofficial' bit:
"How will they know?" Almost certainly, they won't. The USA wants the right to access the criminal records of all visitors to the US. So far most governments, including the UK government, have resisted this. (Canada already lets the US authorities have full access to their criminal database. Many other governments are likely to yield to US pressure in the near future but, at the moment, the UK continues to resist these pressures). The UK does pass on information relating to a number of