Usually they try to trick them with spoofed emails that lead to specially crafted phishing sites, but some of them have lately concentrated on compromising legitimate shopping websites and either stealthily redirecting users to perfectly designed phishing sites, or on modifying the credit card processing file so that it secretly sends the collected card info to an email account or server operated by the crooks.
Sites using the open source e-commerce system Magento have been particularly singled out for these attacks and, in one particular case, the file used for payment handling is altered to replace every occurrence of paymentexpress.com for paymentiexpress.com, a domain owned by the crooks.
According to Sucuri CTO Daniel Cid, the domain has been registered two weeks before and, at the time of writing, it was not blacklisted by anyone except them. The phishing site was so well crafted, that it even had a valid SSL certificate to reassure more careful (or paranoid) users.
"Instead of tricking users into clicking into a bad URL, [the code] tricks the site itself to redirect the users information there," Cid pointed out, calling it an evolution of phishing.
According to Wikipedia, the Magento system is used by some 150,000 online retailers, including big name brands Samsung and Harvey Nichols. Users are advised to be careful when effecting electronic payment, and webmasters are urged to check the code for malicious instructions.