Short question: Can I read credit card information with a NFC capable Windows Phone 8?
Long question: How does NFC with credit cards exatly work? The card (or the phone
Short answer: No. It's unlikely Credit card would work with WP8.
Long answer:
Can I read credit card information with a NFC capable Windows Phone 8?
No, you cannot do that. NFC API on Windows Phone 8 is very limited.
May be Wallet API could help you somehow with your project, but this is not about NFC. Also you could try to use Android devices with NFC, they have more powerful NFC API than WP8.
Contactless credit/debit cards certainly do use NFC (mainly ISO 14443-A, some mainly in France are ISO 14443-B), and their communication protocols follow an industry standard called EMV which has public specs available here: http://www.emvco.com/specifications.aspx?id=223 The cards speak the same EMV both over NFC/contactless as well as through the contact chip (eg the gold thing you insert into a reader) though payment networks tend to do things slightly differently depending on which interface is used (eg sometimes PIN not required via contactless for low amounts, whereas contact might always require a PIN). Also, certain aspects of the protocols are proprietary to the payment networks so the EMV specs don't fully describe everything.
If you search around there are various sites that give some examples of how to communicate with credit/debit cards some over NFC others with an insert chip card, but typically the commands will work the same regardless of the interface. You can buy a USB smart card reader that will do both NFC and insert/contact for http://blog.saush.com/2006/09/08/getting-information-from-an-emv-chip-card/
For Windows Phone you also can talk with credit cards as long as you have a Lumia 830/730/735 etc as the older devices (even the Lumia 930) have an older NFC chip where the driver doesn't support the smart card APIs. You can use the sample code here: https://nfcsmartcardreader.codeplex.com/ to learn how to send/receive APDU commands/responses to NFC cards though that project doesn't specifically have the commands you need for a credit card (though that other link does have the APDUs you need).
And credit cards generally all will let you read their PAN (the account number printed on the front), expiry date, and in some countries even the cardholder name (though in the US for privacy most banks tend to not expose it, instead returning stuff like "VALUED/CARDHOLDER" as the name) without any encryption or keys. It will not however return the CVV2 code printed on the back of the card, which is generally required by merchants to be able to place orders on the internet, and it also generally does not let you clone the card since there is dynamic/encrypted data required to do card present transactions at a physical merchant.
Sorting out a bit of the above answer of JustinAngel: