If you are not working for a very large company with lots of resources, you will need to get a payment provider to handle most of the technical issues. Otherwise you don't want to hold any data on your server that is worth money, since your site will be under permanent attack.
Otherwise the API interfaces of most payment providers I worked with follow more or less the same principles (though actual implementation may vary in many details). When your customer needs to make a payment, you either querry the necessary information (less secure) or redirect him to a secure website of your payment provider (look and feel can be customized in most cases). After that the payment provider will redirect him again back to your website, the route depending on success of the payment. In addition you have ways to query details about the transaction, for example send a request to the payment server and get back some XML (or whatever) that tells you if it was successful or canceled. In most cases this can be implemented in a few days of work.