Internet and phone transaction payments are conducted without the card being in the presence of the vendor. So, if someone has your basic information and card number, they can use it on the Internet. There are ways to protect yourself from online payment fraud. If you are very watchful over your credit card, the chances of your account number being stolen and used on the Internet drop greatly.
First, you want to protect your card number from being stolen. This can happen via dumster diving or online. Magstripe cards can easily be copied, so watch your card carefully during a transaction, and put it back in your wallet immediately after. When buying online, choose Web sites carefully. If you've never heard of the site, do a search and find out if the company is legitimate. Make sure to look for "https" in the URL bar when making a payment transaction (See, How do I know I can trust a Web site?).
Another option is to use a free third party payment tool like PayPal, an eBay company (See, What is PayPal?), instead of giving your credit card information to a Web site.
Lastly, always remember to monitor your credit card statements for any fraudulent activity.