In an instance where one applies for a credit card online with instant approval notification, does it affect one's credit history if they are denied? Also, how do you know beforehand if you will be approved for a particular card?

Applying online is the same as applying offline, except it is much easier and faster. The credit card company will request information from a credit bureau which will create a "hard inquiry" on your credit report. You do not want too many hard inquiries to be reported in a short period of time because this can adversely affect your credit rating.

Whether or not you will be accepted for a specific card really depends on who the credit card is designed for and what your credit profile looks like. If you are applying for low rate cards and you have a limited credit history chances are you will not be accepted. Some cards such as the Nextcard Visa and the Aria Visa will customize an offer to fit your creditworthiness, which increases the chance you will be offered a credit card when you apply.