If you have been to the US before, you probably remember having to fill out a green piece of paper on the flight over there (commonly referred to as the Visa Waiver form) which allows you access to the country without a visa. Well those days are now over. If you're travelling after 12 January 2009 you will need to fill out an online form to request entry to the US instead, at least 3 days before travelling, otherwise you will be turned away by US immigration.
What to do
The application form is available right now on the ESTA's website. It's completely free, so beware of other sites implying there's a fee to pay.
Even if you're only considering going to the States at some point in the future, it's worth filling in the application before buying tickets...just on the off chance you're rejected and can't get your flight/hotel money back.
Each granted application lasts for two years or when your passport expires; whichever happens first. Then you must apply again.
If you don't have access to the internet (then you won't be reading this) then the ESTA suggest that you "contact a friend, family member, colleague or travel agent who is online. Any of those folks are able to fill out the ESTA form on behalf of the traveller."

