Native Instruments provides a separate application to manage all of your installed NI products. That app is called Service Center. This is the app you'll need to open in order to register your new copy of Traktor LE.
So first, lets run the Service Center app. In Windows, you'll find it in Start>Programs>Native Instruments. In OSX, you'll find it in Finder>Applications. Another option is to run Traktor in demo mode (it will open in this mode by default if you have not yet registered), and go to Help>Launch Service Center (this works in both operating systems).
Once Service Center is open, it will look like this...
Notice that there is already an entry field open for you to enter your serial number into. Please find the Traktor LE registration card that came with your SCS controller. On it will be a serial number, and this is the number that goes into the open fields in Service Center. Once you enter the number, press the ACTIVATE button in the bottom right corner of the box.
Your Traktor LE software should now be registered.
Please note that if you have never registered a Native Instruments product before, you will need to create a user account with them PRIOR to inputting your serial number. The Service Center application will guide you through this process. This might seem like a pain at first, but having those details online comes in quite handy. For instance, if you lose the card with your serial number on it, but want to install Traktor LE on a different computer, you can log into the Native Instrument's website and get the serial numbers for all of your registered products (located in the Support>My NI Account area).