If you decide to do things 'by the book', the first two things you'll have to do are to obtain a copy of your police record (from your local police force) and book an appointment at the US embassy in London.
The police officially have up to 40 days to respond to your request for a copy of your record, but they've been known to actually take considerably longer than that.
Well over a month ago, somebody posted on AB to state that the earliest appointment they could get at the US embassy was for late June.
Putting those two things together, it might not be until well into August before you got an appointment at the US embassy, with a copy of your police record. Some people seem to get their visa within a few days but (by accepting a caution for theft) you've admitted to what the US authorities refer to as a 'crime of moral turpitude'. That could mean that it might take at least 3 months, and possibly up to 6, before you heard the result of your application. So it might already be too late to apply for a visa for travel in 2008. Additionally, with a recent offence involving 'moral turpitude', there's quite a high chance that you'd be turned down.
The US authorities have no direct access to UK police records. EU law prevents the UK from allowing the US immigration service to access them. The UK can only pass on specific information relating to individuals convicted of, or suspected of, cross-border crimes such as terrorism, drug-smuggling, etc. If you simply 'forget' about your caution, you'll have no problem entering the USA.
Chris