Before you go live with your osCommerce store, make sure your checkout process page are secure and opening over SSL protocol (https://). Of course you need to have SSL certficate installed on your domain. Before you attempt this, open your store domain over SSL https://www.yourstore.com/ and if it opens fine without any browser warning, your store is ready to go secure.
If it does show warning, or just doesnot open at all, you need to read this first How to Install SSL certificate
You can enable SSL in osCommerce catalog/includes/configure.php file. Set “ENABLE_SSL” to true.
define('HTTPS_SERVER', 'https://www.yourstore.com'); define('ENABLE_SSL', true);
Hope that helps.