How many days/hour does it take to receive an ESTA authorisation since placing online application?
Most ESTA applications are processed in seconds and result in Authorization Approved or Travel Not Authorized. If your application is marked Authorization Pending then it can take up to 72 hours for your application to be processed.
You should check the ESTA web site for the current status of your application, and if it is pending, continue to check periodically.
Source: US Customs and Border Protection