I am not going to repeat on how you need to choose a video driver to install it on your computer, it is written HERE.
Once it so happened that after installing the proprietary drivers and restart the computer, have ended up with a black screen, do not worry. Without leaving the "black screen" make the deletion the driver from your favorite Linux Mint OS:
1. Log in to a virtual console by pressing Ctrl+Alt+F1.
2. After console login enter your username and password.
3. Run the command to uninstall the driver:
sudo apt-get remove nvidia-xxx
Note. Instead of xxx enter the version of the driver installed ( nvidia-340, nvidia-331, etc., which you have installed).
sudo apt-get remove fglrx*
4. After uninstalling the driver restart the computer with the command:
After reboot the system should boot successfully on the free driver.
PS. Commands for use in virtual console you need to remember, and it is better to write down on a piece of paper, because copy nowhere will.