You should create a new page template based on your current page template. Without any example code it is hard to give you a specific example, but here’s an approach:
Copy page.php to a new file and name it page-wide.php. The prefix page- is significant because it triggers WordPress’ template hierarchy.
At the top of this copied page’s source code, make sure the PHP tag begins with something like this:
<?php
/*
Template Name: Custom Page Example
*/
?>
Then, inside WordPress admin, when editing a page, you will have a dropdown box that lets your specify which page template this page should use. It will show up as “Custom Page Example” in the dropdown (in this example).
The point here is that you can create, for example, a page-wide.php, that is almost exactly like your normal page.php but without a sidebar or an extra wide body class which you’ve designed with CSS.