As Jno indicates, you can make an ESTA ("Electronic System for Travel Authorization") application online as long as you qualify for entry under the Visa Waiver Program (which, according to the rules on the US Embassy website, means that you must never have been arrested or convicted of any offence).
If you don't qualify for entry under the Visa Waiver Program you'll have to apply for a visa. The process is complicated, expensive and tedious. You have to obtain details of your police record from the Association of Chief Police Officers and attend an interview at the US Embassy. The process can take several weeks or, if the application has to be referred to Washington, a minimum of 5 months. (The longest wait I've seen reported here on AB was one of 15 months before the guy, who had two convictions for driving with no insurance, was refused a visa).
Chris