It depends on what provider they are using to process your charge and if it's through a website, a phone application or a desktop application.
For example, if they build a desktop application with Authorize.net, the desktop application will take your information in, and then make a webservice call with it to a secure authorize.net processing platform. Something similar is true for FirstData.
However, if they are using PayPal to process your request, you are routed to a paypal site to make the charge, then the funds are sent to the merchant.
As for what is returned that also depends on the provider and the application. If you are using a website it's likely an XML response with all the information they provide upon a transaction attempt. If it's a desktop application they may just hand the cc info off to a library which processes the charge and then returns specific confirmed or denied flags.
So to be totally honest without knowing the exact situation in which you are charging your card, it's impossible to know. For all you know they are putting your credit card information in a database unencrypted and then charging them all at the end of the week in one giant batch.
If you are able to find out whom they are using as a credit card processing provider then you can look for that companies developer documentation. It will provide you with all the information you are looking for including examples.