If your Apache web server is installed on your local machine and you have control of it's configuration, this is really pretty easy.
You will want to set up a VirtualHost configuration for each site domain (whether real or 'made up') that you want to work on. Locate the http.conf file in your Apache/conf directory. Near the bottom will be a sample VirtualHost set up. Pay particular attention to the DocumentRoot directive. You want to point this to the subdirectory where you installed Drupal. Full documentation is available at http://apache.org/docs. If you haven't already, edit your hosts file to point the new domain to your local machine.
Restart your web server and it should allow you to browse to http://example.com. If you still see the subdirectory appended to the browser location, go to your Drupal site folder and edit the settings.php file. Set $base_url = 'http://example.com'; . Now it should work as expected.