Most card companies tell you that it could cost up to $50, but this fee is rarely applied.
The great thing is most credit card companies offer some sort of fraud protection, but make sure you verify it's genuine before you accept it. Some companies make false offers of "insurance" when in fact generally you are already protected by federal law.
Stolen or lost credit cards should be reported in no less than 24 hours, for the zero liability luxury. Once again most major credit card companies rarely enforce this requirement either. But regardless you should always get on the phone the second you feel your card was stolen or lost, or you feel there are charges that you never ran up.
Follow the call with a written and signed letter stating the phantom charges that occurred, also include the details of whom you spoke with etc. Its better to be safe than sorry when dealing with theft.
Make sure when receiving your credit card you read all the fine print in detail, because there are always exceptions. Most companies that offer protection are likely to reject you if you have done something reckless with the card, for instance not reporting the card after a while when you "thought" it was lost or stolen.
In essence when you apply for a credit card find a trustworthy bank. Like american express, chase, bank of america, or any visa and mastercard. This way you know that you have a understanding reliable company to back you up when theft occurs.
Richard Gilliland Provides comparison resources for all major credit card companies at http://www.credit-wisdom.com