In order to configure osCommerce to work with SSL you should open the file public_html/catalog/includes/configure.php and make the following changes:
define('HTTP_SERVER', 'http://www.yourdomain.com'); // eg, http://localhost - should not be empty for productive servers
define('HTTPS_SERVER', 'https://yourdomain.com'); // eg, https://localhost - should not be empty for productive servers
define('ENABLE_SSL', true); // secure webserver for checkout procedure
define('HTTP_COOKIE_DOMAIN', 'www.yourdomain.com');
define('HTTPS_COOKIE_DOMAIN', 'yourdomain.com');
define('HTTP_COOKIE_PATH', '/catalog/');
define('HTTPS_COOKIE_PATH', '/catalog/');
define('DIR_WS_HTTP_CATALOG', '/catalog/');
define('DIR_WS_HTTPS_CATALOG', '/catalog/');
Similar to the above changes have to be made in the file public_html/catalog/admin/includes/configure.php which is responsible for the admin area configuration.
In the above example we are configuring an osCommerce installation in the catalog directory with domain yourdomain.com. You should adjust the above settings to your details.
If you are having problems configuring osCommerce to work with SSL, contact your host for assistance. SiteGround provides the best osCommerce hosting and such requests are handled with ease.