The Submission Receipts feature is what you're looking for. The following post describes the feature in detail:
Let me know if you have any additional questions.
I used that and test submitted and it did not send the same copy that I get as the administrator. We are using for an internal program.
Is the problem that the submitter didn't get an email at all? Or that they got something different?
The form authors get a standard Submission Notification email from FormsCentral indicating the new response. The Submission Receipt email to the submitter is something that you can customize.
My mistake – looks like I got it.