Don’t confuse WordPress templates: header.php, sidebar.php, and ect., as layout/graphical representation of your website. These files are about HTML document structure, not layout. You can moch-up your page however you like.
header.php – from html doctype to body tag
index.php – from body tag to footer tag
footer.php – from footer tag to end of document
Then your index.php would require all the necessary parts to form HTML document, like so…
// beginning of index.php
// your layout, html that makes up your app
// look into WordPress loop, it’s what interacts with the database and get’s all the appropriate data into the template.
//end of index.php
Actually, you can just have index.php and your style.css file and your site will work. See [Template Hierarchy](http://codex.wordpress.org/Template_Hierarchy).
Hope that helps