What exactly do you want to exclude from the header and footer, if you conditionalise them out, you'll not have a complete document, since the primary HTML markup is missing, notably the opening/closing HTML and BODY tags.
What you should do is open up both the header.php and footer.php, and place these two pieces of code around the code you want to conditionally disable for a set page.. (1 is an example ID)
<?php if( !is_page( '1' ) ) : ?>
and
<?php endif; ?>
Which basically means, when it's not a page with the ID 1, then execute the code... (so basically it's not shown if it is page with an ID of 1).
This is exactly what esmi was suggesting in her response.
If you can't manage it, open the 2 files (header and footer), and paste them into individual pastebins, and post the links back here, and i'll write in the conditions for you... ;)