Depending on your home page, you either can set up a template file home.php (archive) or front-page.php (static page). In the according file, you can do whatever you want. Run additional queries, load content from whatever source etc.
If this is not what you want, then you can have a look at the template_include filter hook.
If you want/need to do more than just load a specific template file, you might want to have a look at the template_redirect action hook.