I have seen two type of card readers:
1 - plugs into your keyboard port and acts as a keyboard (can also plug into a USB port, but still simulates a keyboard). When a card is swiped the info is written to whatever application and text field currently has focus.
2 - Has some kind of hardware driver (most likely a USB driver, possibly Serial or other).
If you aren't sure which you have then open notepad, make sure it has focus, and swipe the card. If the details show in notepad then you have #1. If they don't, then you probably have #2
If your reader is #1 then you can put some code into the Textbox's TextChanged event to do what you need (I presume you can add code to the application as you said you are building it).
If your reader is #2 then it really depends on the driver it uses. Some will likely provide an API you can integrate with, but you will need to find documentation.
Do you have a model number and manufacturer for your card reader?