If you're apprehensive about sharing your credit card information online, you most definitely cannot be blamed for it. It's rather obvious that when it isn't handled carefully, credit card information can be misused by various parties to cause decent damage to your bank account. A good way to keep your credit card information safe online is by following the tips shared here.
The most important tip would be to share your credit card information only on well reputed and well known websites. For example, you can register your card on Apple's website, you know it's safe to provide them information and that it will be dealt with responsibly. Then again if you're still worried, then you can register online for fraud prevention solutions. These are usually offered by banks and other financial institutions that you are associated with. A good idea would be to avoid sharing any financial information online via email primarily because emails are the easiest to intercept. The best option when it comes to using your credit card online would be to ask for a virtual or alternate credit card number, sometimes your financial service provider will provide you such a service which will in turn serve as a sort of a passcode allowing a onetime access to your account.
Other ways include creating intermediary accounts such as a PayPal account. PayPal will also be using your credit card but by redirecting it via a PayPal account it's like creating a safety net. Never click on any unknown link or provide information to people who may claim to be offering you a prize money of some sort that just doesn't happen- don't get scammed, don't share information, and inform your bank to give you a regular update on your statements, or send a text for transaction so that if there is any malpractice you can immediately block your card. Also, always use the virtual keyboard. Be sensible, because the web is only what you make of it.