I am using After Effects in CC 2014 and I thought that color finesse came with the download for free but the trial mode is all that I can see and when I download the installer it asks for a serial number that I do not have. Any suggestions to fix this problem?
You didn't need to download an installer. Color Finesse is automatically installed by the Adobe AE installer. It is automatically serialized (in CS5.5 and later, including CC 2014) the first time you apply Color Finesse to a layer.
The best approach at this point is to uninstall and re-install After Effects. Then open a project, apply Color Finesse to a layer, enter your name, and you'll be up and running.