First of all, what do you mean by "user submits the form"? The term "submit" means that the data is sent to server and processed via server-side scripts.
If you just want to send the values from pop-up to parent page, it's a different story. You can do it, for example, by simple variables assigning:
window.opener.var1 = document.formName.field1.value;
This will assign the value of some form field from pop-up to variable in parent page named 'var1'.
If this is what you need, just do the same for all desired fields, and close the popup:
function sendAndClose(){
window.opener.var1 = document.formName.field1.value;
window.opener.var2 = document.formName.field2.value;
. . .
self.close();
}
. . .
<input type="button" onclick="sendAndClose()">
Before that it's a good idea to initialize all necessary variables in parent page:
var var1;
var var2;
. . .