You can enable email notices when you add or modify your event in the invitation manager. You will see an option for 'Would you like to receive an email when someone responds?' The default for this option is no but you can select whether you want to receive an email each time someone responds or to only receive an email once per day when there is a response.
An advantage of selecting the first option is that the email will contain the person's full event registration information. The latter option is usually selected when people have a very large guest list. The email that is sent with this option does not contain event registration information.