First-of-all, you should make sure that you really need those proprietary drivers. If you're happy with your current performance with Nouveau in use - just don't touch it. Nouveau drivers are updating, while legacy proprietary drivers from NVIDIA (340.xx) aren't.

Second-of-all, make sure that you didn't try to install these manually via other 3rd-party PPAs or even official .run from NVIDIA (installing that requires A LOT OF EFFORT and surely the method of it's installation is far outdated). If you did, and especially were half-way on installing .run from NVIDIA then proceed really carefully. You can end up with unbootable system, that just blinks underscore and refuses to load.

So, setup I recommend to proceed with is:

• some legacy NVIDIA videocard plugged in (like GeForce 210)
• freshly installed Linux Mint 21, without anything done with videodrivers
• bad performance with Nouveau (so you really need proprietary ones)
• driver manager not showing you proprietary NVIDIA videodrivers (cause they aren't updating and considered legacy)

Now, let's get started:

1. Go to the NVIDIA official site and go to their driver downloader. Enter your videocard, and if you ended up with "340.xx", then you're good and we can proceed. If it's not, that's not a tutorial you need.
2. Add PPA with 340 drivers from kelebek333. You can do it by these commands (open your Terminal and copy-past these): 

   sudo add-apt-repository ppa:kelebek333/nvidia-legacy
   sudo apt update

3. Now, install drivers from this PPA with following command: 

   sudo apt install nvidia-340 xorg-modulepath-fix

4. After it's done, restart your computer. At startup you should see that mint logo became bigger: it's OK, just normal NVIDIA drivers behaviour.

And finally, if after installing proprietary drivers you'll need to switch those to Nouveau (or some weird package will switch them for you on installation process) just open your Driver Manager and it will show avaivable options.