From experience I recommend not installing the drivers from the Nvidia site, but instead use the PPA from Swat-X located here: https://launchpad.net/~ubuntu-x-swat/+archive/x-updates
Go to a terminal and type the following:
sudo apt-add-repository ppa:ubuntu-x-swat/x-updates
sudo apt-get update
Then depending on your video card (Ati, Nvidia, Intel) you should either receive an update (If you have Intel or have already installed an Nvidia o Ati driver from the Additional Drivers) or you should install the driver manually since for some people like you and me, Additional Drivers is not working correctly (Bugs Here, Here and Here for example). What you should do is AFTER installing the X-Swat PPA, install the Nvidia package from the terminal or Synaptic (Since Software Center also gives the error).
sudo apt-get install nvidia-current
The latest version in the X-Swat PPA supports the GTX 680 (Which is the 304.51 version as of this writing).
Now you ask why I do not recommend using the Nvidia drivers from their site, the basic reason is that the X-Swat team has tested the version they have (Which tends to be the latest Nvidia driver) in Ubuntu, so you have a better guarantee that it will work. With the Nvidia site driver, you not only don't get new updates when a new one comes out, but it is a more general Linux package that it is not tested on Ubuntu as much as the one in the X-Swat PPA. You basically save time, get updates and be more on the safe side when using the PPA than the one from the Nvidia site, which is to not say their version is bad, it is just less focused on Ubuntu than the actual one tested in the PPA. I am removing the Additional Drivers from the comparison because of the Bugs.
Now for the part about the errors. Follow this steps to make sure you have a clean system before installing the Nvidia drivers the way I have tested them to work:
If you installed the Nvidia driver from the Nvidia site type the following on the terminal (Assuming you have the Ubuntu 64Bit with the 304.51 version of Nvidia):
sudo sh NVIDIA-Linux-x86_64-304.51.run --unistall
If you have install any nvidia package like
nvidia-current-updates remove them.
sudo apt-get remove nvidia-current for example.
ANY change you did to blacklist the Nvidia driver for instance or changes to any other files related to the Nvidia driver should be reversed. This is just in case you went ahead and started editing like crazy (Which happens I know ^^).
Delete or backup/move the
xorg.conf file. You will not need this file right now.
Reboot the PC and make sure it loads with Nouveau and not with any Nvidia drivers.
If right now you KNOW you are running unity on Nouveau OR if you just happened to get a video error or it just fails to correctly load LightDM, do not worry, all 3 options will end the same way. When rebooting, in the GRUB menu, select the "Recovery Mode". After the recovery mode shows you the recover options choose the root option or the Failsafe X option. In this modes and after all previous steps have been done, install the nvidia driver using the PPA I mentioned above.
sudo apt-get install nvidia-current. Remember there should not be anything installed before doing this in regards to Nvidia (Except obviously the Nouveau drivers).
Now reboot and all should work. If not let me know since there is one more way but I would actually have to sabotage my own PC to do it.
Change the first time the resolutions using the Display Settings option in the System Settings part of Ubuntu (Top Right corner where the little Cog icon is).
If using the Nvidia-Settings within Unity, when yo try to save the settings to the xorg.conf file it will throw an error but give you the option to insert your sudo password to create the xorg file correctly. This will only happen the first time. You can also just run the nvidia-xconfig but only as the last step in all of this.
NOTE - In Step 6, if it looks as though the PC is stuck loading just press CTRL+ALT+F1 to go to the TTY1 terminal and do step 6 from there.
You should know that even after doing all that, Additional Drivers will STILL say you are not using any Nvidia Drivers (Another bug) but do not worry since the Nvidia card will work correctly.