This was surprisingly easy to do:
1. Root the Phone
This was made simple thanks to Towel Root. Please see https://towelroot.com/ for this easy to use utility. Afterwards you can confirm that your phone is properly rooted using Root Checker.
2. Install a Custom Recovery
Once rooted this was too easy. Install TWRP Manager making sure to install BusyBox if required. TWRP Manager will manage everything so just follow the instructions and you’ll be good to go. If you get any BusyBox errors fret not, install the supported Stericson BusyBox.
There’s no tool like Titanium Backup. Install it, buy the Pro key, and back up your user apps and data. Later in Restore Apps & Data you will be able to quickly restore your apps and their config data saving you countless hours of tedious effort. It will also back up and restore your Hangouts/SMS messages.
But possibly more important than backing up your apps & data is making a nandroid backup of your original system. This will allow you to restore your phone to its pre-CyanogenMod state, Samsung’s infamous KNOX warranty bit notwithstanding. Simply reboot to recovery by powering down your phone then powering it up by holding down the power button, home screen button, AND volume up at the same time until the Samsung logo appears. Then select Backup and select what you want to back up. I recommend Boot, System, Data, EFS, and Modem. Once the backup is complete, make sure you copy the files off your phone onto a PC.
Important: both of these backups should go to the SD card so they can be restored later if need be.
I also recommend connecting your phone to your PC and manually backing up photos, videos, etc. These are NOT captured in the above backups. Note that your external SD card will not be affected by the upcoming erase and flash operations unless you do something really goofy.
4. Download the Files
The latest CyanogenMod 12 files are located here. Select the latest Nightly build but understand the risks in doing so. As of this writing there is nothing more stable than Nightly builds but eventually there should be something better.
You will also need the Google Apps package which will allow you to use the Play Store etc.
These two ZIP files should be saved to your external SD card. I use a folder called ROMs for anything I might want to flash.
Flash the Phone
Now that you’re all backed up and no longer afraid to lose anything on your phone, it’s time to leave TouchWiz. Boot into recovery. From here you should do a Wipe/Factory Reset, then select Install. Navigate to your ZIP files and first add the CM12 file followed by the Google Apps file, then flash them. This shouldn’t take very long and once it’s finished, clear the Dalvik cache when you get the chance. Then reboot into CyanogenMod and configure your new phone.
Warning: make sure you have a fully charged battery. The last thing you want is for the battery to exhaust itself in the middle of a flash…
Restore Apps & Data
If you choose to allow it when initially setting up your new phone OS, CM12 will start re-installing your apps. If Titanium Backup was not installed then install it. After launching it you can select Restore and select which apps and/or data to restore. If your apps were automatically re-installed for you then you only need to restore their data.
This restore process works very nicely and allows you to quickly restore your applications’ states without having to manually reconfigure them one by one.