Ensure you have a backup of your W8 system, just in case.
Pop the Linux Mint CD / DVD in and reboot - boot from CD
Follow the on screen instructions and accept the option to "Install alongside existing OS" - this will give you a dual boot option.
At the last step it will ask about the bootloader and if you want to be able to boot W8 - ensure it is ticked. Linux Mint will probably be the default OS to boot but this can be changed once installed.
(If you have a second HDD I would pop it in and install Mint to it, this avoids changing the W8 partition)