Dear friend,

There are two ways of doing it. One on the client side and the other one is server side.

On client side, you javascript's method Onblur event of textBox and call a javascript method that gets value from one TextBox and sets the value in second one. So the code like following:

<input type="text" id="register" OnBlur="SetExpiryDate()" />
<input type="text" id="expired" value="" />

and in head section of page add:
<script language="javascript">
//assuming dates are seperated by '/' and is in MM/DD/YYYY
var Date1Split = document.getElementById('register').value.split('/');
var dte = new Date;
dte.setMonth(dte[0]);
dte.setDate(dte[1]);
dte.setFullYear(dte[2]);
//Calculate the expiry date
var expiryDate ;//add logic to calculate the expiry date..left for u

//set the text of textBox expire
document.getElementById('register').value = expiryDate.getMonth() + '/' + expiryDate.getDate() + '/' + expiryDate.getFullYear();
</script>

on server side you can do it easily by adding an event handler, or by just calling post back to page on OnBlur Event by calling __doPostBack('','');

and on server side do expire.Value = DateTime.Parse(register.Value).AddDaye(30).ToShortString();

Hope this helps