My WordPress theme didn’t have a 404.php page included and I wanted to make any error 404 “page not found” go to the home page. This method would go to any page you specify. This is a somewhat hard coded solution and it is a permanent redirect in this case.
Contents of 404.php:
<?php
header("Status: 301 Moved Permanently");
header("Location:http://www.mywebsite.com");
?>