We have set up a number of websites over the years that take payments through the site using a third party to process the credit card information. A common third party supplier is Opayo (formerly SagePay), who process the shopping basket or other payment items the website passes through. This involved send through the information from the website to secure pages on the SagePay website. The down side to this is although you could apply basic styling to these pages, they would always look very different to your website. What you are able to do now is embed an iFrame into your website to load up the SagePay credit card forms, passing in the same information and process the details in the same way. The advantage to this is the customer remains on your site and as you are able to style the SagePay forms so they can blend seamlessly into your site.