Because you don't use ONCLICK with a submit button, you need to use forms, submit button is for submitting forms.
<form name="example" method="post" action="page.php">
<!-- Put other fields here -->
<input type="submit" Value="Process Reservation" />
</form>
Although I don't know why you would submit a form without having any fields, other than submit.
Than once it gets to the php page and you want it to redirect use:
header('Location: page.html');