When you see the grub menu use the "e" key to "edit" the entry for just the one boot. Go to the line that will look something like
Yours may look a bit different but there will be a line with quiet splash in there at the end. With the cursor keys go to that line and delete those two words and replace with nomodeset then hit Ctrl+X to try to boot.
linux /boot/vmlinuz-3.5.0-46-generic root=UUID=1fd42bfe-b5d4-4389-9607-1207af1c3e8b ro quiet splash $vt_handoff
With luck you will get a GUI and you can then fully update the OS and look for a driver for the graphic card using the Additional Drivers utility, which you can get to if you cant find it in the menu by using the command /usr/bin/jockey-gtk in terminal.
There are many other boot options available but that is the most likely to get you going. Once the new graphic driver is installed you may not need any further actions for future boots.