If you're looking to have it automatically add up without a page refresh or submit button clicked you'd need to use Javascript & AJAX.
Otherwise your form could look like this:
<form method="post" action="index.php">
<input type="text" name="field_1" /> First Number<br />
<input type="text" name="field_2" /> Second Number<br />
<input type="submit" />
</form>
on the index.php file in the header you would do this:
<?php
$val = $_POST['field_1'] + $_POST['field_2'];
echo $val;
?>