When you use Paypal or other externally hosted gateways your user is taken to a different website to complete the transaction. If you want to have your users not leave your site through the entire buying process you will need to:
To enable SSL services on your site you will need enable SSL (secure socket layer). You can self sign an certificate or use an externally signed SSL certificate that provides your customer some assurance of safety when shopping online. You can buy SSL certificates from $10/year to many thousands of dollars. Your vendor will be able to assist you in installing an SSL certificate.
Once you establish a merchant account for your bank account, you will be able to use Worldpay, authorize.net or other payment gateways that allow you to process transactions on your site with the customer never leaving your website.
Resources
Video
In this video you will see how to enable payment through a third party gateway using SSL
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