TL;DR: if you bought anything from Newegg between August 14th and September 18th, call your bank and get a new credit card. You can find more details in these articles: NewEgg cracked in breach, hosted card-stealing code within its own checkout | Ars Technica // Hackers stole customer credit cards in Newegg data breach | TechCrunch // Magecart Strikes Again: Newegg in the Crosshairs | Volexity // Another Victim of the Magecart Assault Emerges: Newegg
The credit-card skimming attack appears to have been done by Magecart, the organization behind earlier attacks on British Airways and Ticketmaster. If you are one of the customers victimized by one of these attacks, it's not your fault, and there isn't much you could have done to protect yourself (but read on for some tips). Sorry about that.
This article, Compromised E-commerce Sites Lead to "Magecart", gives some useful advice. (It's way at the end, of course; search for "Conclusion and Guidance".) The most relevant for users is
An effective control that can prevent attacks such as Magecart is the use of web content whitelisting plugins such as NoScript (for Mozilla’s Firefox). These types of add-ons function by allowing the end user to specify which websites are “trusted” and prevents the execution of scripts and other high-risk web content. Using such a tool, the malicious sites hosting the credit card stealer scripts would not be loaded by the browser, preventing the script logic from accessing payment card details.
Note that I haven't tried NoScript myself -- yet. I'll give you a review when I do. They also advise selecting your online retailers carefully, but I'm not sure I'd consider, say, British Airlines to be all that dubious. (Ticketmaster is another matter.)
Shy away from sites that require entering payment details on their own page. Instead prefer the websites that send you to a payment organization (PayPal, payment gateway, bank, etc) to complete the purchase. These payment organizations are required to have very strict security policies on their websites, with regular assessments, so they are less likely to be hacked or miss some unauthorized modifications in their backend code.
They also suggest checking to see whether the website has had recent security issues, and using credit cards with additional levels of authentication (e.g. 2FA -- two-factor authentication).
Things are more difficult for retailers, but the best advice (from this article, again) is
Stay away from processing payment details on your site. If your site never has access to clients’ payment details, it can’t be used to steal them even if it is hacked. Just outsource payments to some trusted third-party service as PayPal, Stripe, Google Wallet, Authorize.net, etc.
Which is the flip side of what they recommend for shoppers. If the credit card info isn't collected on your site, you're not completely safe, but it avoids many of the problems, including Magecart. Keep your site patched anyway.
If you insist on taking payment info on your own site, and even if you don't, the high-order bit is this paragraph:
E-commerce site administrators must ensure familiarity and conformance to recommended security controls and best practices related to e-commerce, and particularly, the software packages utilized. All operating system software and web stack software must be kept up to date. It is critical to remain abreast of security advisories from the software developers and to ensure that appropriate patch application follows, not only for the core package but also third-party plugins and related components. [emphasis mine]
@ NewEgg cracked in breach, hosted card-stealing code within its own checkout | Ars Hackers stole customer credit cards in Newegg data breach | TechCrunch Magecart Strikes Again: Newegg in the Crosshairs | Volexity Another Victim of the Magecart Assault Emerges: Newegg Inside and Beyond Ticketmaster: the Many Breaches of Magecart The British Airways Breach: How Magecart Claimed 380,000 Victims Impacts of a Hack on a Magento Ecommerce Website