According to the rules on the US Embassy website, you're ineligible to travel under the Visa Waiver Program. That means that you must apply for a visa. The application process is lengthy, tedious and fairly expensive; it involves getting hold of a copy of your 'record' from your local police force and attending an interview in London.
If the offence for which you were convicted falls within the category of 'moral turpitude' (which includes even the most minor thefts but excludes most assaults) then the US Embassy must, in the first instance, refuse to issue you with a visa (since the US Immigration and Nationality Act places a lifetime bar on anyone convicted of an offence of moral turpitude entering their country, other than in very limited circumstances). However the application can then be referred to Washington as an application for a 'waiver of permanent ineligibility'. If such a waiver is granted then the US Embassy can issue a visa (but is not obliged to do so)
So offences of 'moral turpitude' can involve lengthy visa processing times. The MINIMUM period is usually around 5 months but the longest wait that I've seen reported here on AB was one of 15 months (from someone who was eventually refused a visa because of two offences of driving without insurance).
If 'moral turpitude' applies in your case it's possibly already too late to get a visa (and then to book your holiday) for 2012. It might be better to consider the second half of 2013 as a possible travel date.
See here for further information about what counts as moral turpitude:
http://en.wikipedia.org/wiki/Moral_turpitude
If your offence is not classed as 'moral turpitude' you'll still have to wait several weeks to get hold of your 'record' and for an appointment at the US Embassy but you'll probably hear the result of your application within around a week after that. The UK's Rehabilitation of Offenders Act isn't recognised by the US authorities, so offences can never become 'spent' however I've seen indications posted here (based upon what people have been told when they've attended their interviews at the Embassy) that visas are generally refused unless a minimum of 5 years has passed since the end of any punishment imposed by a court for the offence. Thereafter a visa MIGHT be granted but it depends upon the individual circumstances.
Some people have successfully entered the USA by 'forgetting' about their convictions and (illegally) using the Visa Waiver Program (with an 'ESTA'). The US authorities have no DIRECT access to UK criminal records but they do seem to know quite a good deal about individual travellers. Some people have been stopped at immigration, held in the cells until the next flight home, put on that flight and then billed for the cost of the tickets.
Chris