(2-part post):
The US embassy website states that anyone who has been arrested (which usually precedes a caution) is ineligible for the Visa Waiver Program and must therefore apply for the a visa. The process is extremely long-winded and can take 5 or 6 months. See here for details of the procedure:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
However, the actual visa waiver form (which travellers complete on the aircraft) doesn't ask about arrests. It only asks about
convictions for crimes 'of moral turpitude'. (A caution is not a conviction so, irrespective of the type of crime involved, there would be no need to declare it). Additionally, the US authorities have no direct access to UK criminal records, so they wouldn't know about the caution.
Accordingly, your daughter's friend should have no problems entering the USA under the Visa Waiver Program, even though this would actually be in contravention of the rules on the US embassy website.
However, it should be noted that entry under the VWP does not grant anyone the right to work in the USA. A separate visa would be needed for this. Such visas are generally only available to people who have skills or talents which can't be provided by a US citizen. (e.g. leading film stars or talented brain surgeons). Your daughter and her friend will not be permitted to work in the USA.