First of all, you need to make sure Lightroom CC(2015) is downloaded and installed on your machine. If not, you can open Creative Cloud App from your programs or applications list and click on Apps panel and install Lightroom CC(2015) from there.
After installation, when you will launch Lightroom CC(2015) for the first time, it will ask you to upgrade your previous Lightroom catalog to CC(2015) version and you may choose the option to upgrade the catalog.
LR 6 is the standalone upgrade. If you are a creative cloud subscriber then you will want to install the upgrade which is called Lightroom CC. It is available from the creative cloud application manager. If you don't see it listed as an available install, signout from the application manager and then sign back in.
I have tried uninstalling LR then downloading the 'upgrade' and every time it reverts back to the trial version. I cannot seem to convert this to a non-trial version. I understand that LR 6 is a standalone but because I cannot seem to get LR CC 2015 in a version other than trial, I thought about buying LR6 standalone. What to do?
If you are a subscriber, did you do as Jim suggested? Launch Creative cloud and click on the settings icon (cogwheel near top right) and sign-out. Then close Creative Cloud and re-launch. Sign-in again and go to the Apps tab. The applications should have refreshed. If so click the Install button next to Lightroom CC 2015.