Here's my solution. I had to pull answers from several locations.
My graphics card is the NVidia GeForce GTX 950.
The first thing I did was download the latest stable NVidia driver from nvidia.com (for me, it was 361.42). I was sure to select the latest stable and certified driver. It's a ".run" file, by the way. Search on how to install .run files if you're not familiar with this.
I then blacklisted the Nouveau drivers according to this post (my steps are below and are slightly different from this post):
Install Nvidia driver instead nouveau
I did all of my work through the virtual terminal accessed by Ctrl+Alt+F1 from the log in screen:
1) Blacklist the modules. Open the blacklist.conf file.
sudo vi /etc/modprobe.d/blacklist.conf
add the following modules to the end of the file:
Save the file and exit.
2) Remove all the nvidia* packages (note this didn't do anything for me, but it's recommended. No harm done in running it)
sudo apt-get remove --purge nvidia*
3) Update the initramfs disk. Mine was configured to load the nouveau drivers. It takes several seconds. Don't reboot or poweroff!
sudo update-initramfs -u
5) Stop the display manager and then install.
At the login screen press Ctrl+Alt+F1 again to get into the virtual terminal. Once you are in the text mode, stop the display manager:
sudo service lightdm stop
6) Then, run the installation file (the .run file you downloaded). The installation is well documented and contains lots of useful messages along the way (imagine that!). I did get the error about the pre-install script failing. I continued anyway. I got asked "Would you like to run the nvidia-xconfig utility to automatically update your X configuration file so that the NVIDIA X driver will be used when you restart X? Any pre-existing X configuration file will be backed up" I answered "Yes" and continued. I have a 64-bit system and got 32-bit errors. I didn't worry about it and continued. The 64-bit ones installed fine. I got to the end of the installation!
7) Cross your fingers, reboot, and log in. My system FINALLY came up. I hope yours does too!