Your profile says you are in the UK. If you are a UK citizen, without a criminal record, you probably would be eligible to enter the US under the Visa Waiver Program—no visa needed. However, with a criminal record, you will need to apply for a full B2 tourist visa. The US Embasdy in London says:
If you have ever been arrested and/or convicted or cautioned of an offense anywhere in the world, we recommend that you apply for a visa before traveling to the United States. Please note that the Rehabilitation of Offenders Act does not apply to U.S. visa law. You are required to declare the arrest/caution/conviction, regardless of when it occurred and your age at the time. Further information on applying for a visa and the documents required in support of the visa application is available here
If the offense is fairly minor, it is likely that you would be granted a visa, but you will have to show that it was indeed minor and that you have been a good citizen since then. Give yourself plenty of time—a couple of months or more—for Visa processing.
P.S. I have asked the moderators to move this to the US branch