How do I create a customer loyalty program using a credit card?

I came across a site called zavee, and the site lets you use a credit card as a points reward card. I want to do the same but I don't understand how to do so. Even if I do obtain credit card numbers, how would I use that to track if the user buys from a specified place. A friend suggested that I should just use a system that compares the sales table of the location to the stored credit numbers to see if any match and then award point accordingly. But I think there's a better way, I just can't think of how. Would someone have some extra clues to help direct me?

Basically these type of sites are partnered with retailers. Only thing I can say is you will have to be very careful (and knowledgeable) if you attempt this. Storing credit card information is a huge responsibility under law. If something goes wrong, your server gets hacked and credit card information is stolen, you will be in very deep trouble. Since you are in USA, be VERY CAREFUL.