You have to disable secureboot before you do anything else. I think it's usually an option in the BIOS menu. Look for tutorials for your particular system. Once you do that, you can do pretty much anything. If you want to keep windows 8, use it's built-in disk management utility to make room for Linux. To install Mint with EFI, you should use a Mint 14 disc or USB (I prefer USB for speed and convenience) and you must boot it via EFI instead of BIOS. Again, find a tutorial for your system. If you boot the LiveUSB via EFI, it will install everything needed to work with EFI.
If you want to use Windows 7 instead of 8, I would still recommend an EFI install. You can use Mint to partition your disk, install Windows 7, then install Mint. Make sure to partition your disk with GPT instead of MBR. Gparted supports both.
Running on a 4-slot toaster @ 60Hz