Since you mention Cinema 4d I'm going to assume you're using CC, although this applies back to AE CS5.5.
Color Finesse is installed into After Effects automatically. The first time you apply it to a layer you'll be asked for name and (optional) organization. It won't ask for a serial number because that is all handled "behind the scenes." (If you ever need your Color Finesse serial number--such as when upgrading--you can click the Color Finesse "About" button and find it,)
If you're being asked for a serial number then you must be running a version of Color Finesse other than the one included with After Effects, such as one downloaded from our web site. That's fine, but you will need your serial number (see above). If you're being asked for the serial number when starting AE, then you must be opening a project which uses Color Finesse. Try launching AE with Caps Lock on to prevent Color Finesse from being invoked.
If you post a screenshot of the dialog you're getting it may offer more clues as to what is going on.