As NogDog says, you'd most likely want to use sessions. This can be accomplished by submitting your form to a php script that adds the values into a session array.
<form method="post" action="process.php">
<input type="text" name="field1" />
<input type="submit" value="Send!" />
$_SESSION['field1_val'] = $_POST['field1']; // This value can now be accessed on PHP pages.
// Nothing can be outputted before this point or you'll get errors.
// Basically don't try to echo stuff. :P
echo 'This is the final destination after submitting the form.<br />';