Travelers from certain countries can apply travel authorization, so called ESTA. Those countries who participate the US Visa Waiver Program include: Andorra, Australia, Austria, Belgium, Sweden, Italy, Finland, Denmark and so on. See the full list of US Visa Waiver Program here.
ESTA is usually issued within 48 hours after the submission of the application. On the application form, make sure you write your first given name exact according to your passport, not all the given names, not the given names that you are using in the daily life.
ESTA to the US is electronic, all of your passport details is going to be registered in the US Customs and Border Protection. Usually after your application gets approved, you will receive an email with ESTA details. In fact, all the information on the detailed letter is your passport information except the application number and the expiration date. So you do not need to print out anything. At the airport, as soon as you show your passport, the passport control or border control is able to see you have a valid ESTA to the US.
If anything goes wrong, you have to contact US Customs and Border Protection, local American embassies cannot assist you in any way when it comes to ESTA. Usually the reason that your ESTA application get denied is because: you had US visa canceled in the history, you had conducted drug related crimes or suffering from one infectious disease. As soon as your application get denied, you are no longer eligible to apply ESTA anymore. The only way to get to the US is going to be applying for a visa from the local American embassies.
ESTA is usually valid for 2 years or as long as your passport validity. During those 2 years, if the previous circumstance remains the same, for example, you are using the same passport, you did not have any US visa canceled, you are able to use the same ESTA.
If you are not from those US Visa Waiver Program, you have to apply for a visa from the local American embassy, which can take much longer time since you have to book a time for an interview. Therefore we suggest all the travelers to start the visa application process as soon as the trip is decided.