Rick Strahl has published a excellent (and very comprehensive) new article on techniques to perform credit-card payment processing with ASP.NET. He also includes full source code examples (for both ASP.NET 1.1 and ASP.NET 2.0). You can check it out here.
If you are interested in ecommerce, then you should also check out the ASP.NET 2.0 PayPal-enabled Store Starter Kit that you can download for free from here (it is near the middle of the page). It provides a really easy way to get an e-commerce site up and running using ASP.NET 2.0, and has PayPal payment integration built-in.
Hope this helps,