One way of doing this is to go to the Nvidia website and download the latest file from the relevant page on there. Then, the next stage is to restart your PC and choose rescue mode instead of the more usual graphical option. This drops you onto a command shell that is requesting your root password. Once this is done, you can move onto the next stage of the exercise. Migrate to the directory where the *.run file is located and issuing a command similar to the following:
bash NVIDIA-Linux-x86_64-295.40.run
The above was the latest file available at the time of writing so the name may have changed by the time that you read this. If the executable asks to modify your X configuration file, I believe that the best course is to let it do that. Editing it yourself or running nvidia-xconfig are alternative approaches if you so prefer.
Proprietary Nvidia drivers are included the repositories for Linux Mint Debian Edition so that may be a better course of action since you will get updates through normal system update channels. Then, the course of action is to start by issuing the following installation comands:
sudo apt-get install module-assistant
sudo apt-get install nvidia-kernel-common
sudo apt-get install nvidia-glx
sudo apt-get install kernel-source-NVIDIA
sudo apt-get install nvidia-xconfig
Once those have completed, issuing the following in turn will complete the job ahead of a reboot:
sudo m-a a-i nvidia
sudo modprobe nvidia
sudo nvidia-xconfig
If you reboot before running the above like I did, you will get a black screen with a flashing cursor instead of a full desktop because X failed to load. Then, the remedy is to reboot the machine and choose the rescue mode option, provide the root password and issue the three commands (at this point, the sudo prefix can be dropped because it’s unneeded) then. Another reboot will see order restored and the new driver in place. Running the following at that point will do a check on things as will be the general appearance of everything:
glxinfo | grep render