Supposing you have created a read only field called “todayDate” and formatted it as date, you need to create a document level JavaScript, using Adobe Acrobat Pro, to change the value of the field when the PDF is opened. In Acrobat XI Pro go to menu View -> Tools -> JavaScript:

Click on “Document JavaScripts” and add the following code:
function dateToday() {
var d = new Date();
f = this.getField("todayDate");
f.value = d;
}
dateToday();
When the document is opened the dateToday() function is loaded and executed.
If you want the “todayDate” field to be updated when the form is reset, you can call the dateToday() function in the Custom Calculation Script of the “todayDate” field.

