the general idea is this:
1. backup your files !!! make more than one copy, this can be to a usb flash drive, external hdd/ssd, online (cloud) storage etc
2. in Windows 8, in power options, disable the option for hibernation as shutdown method.
3. download the linux systems you might use, best to get a couple, in case you make a mistake, and one isnt compatible enough or something.
http://www.linuxmint.com/oldreleases.php
(the xfce edition is light, plenty of options, very customisable, doesnt require fancy graphics)
https://www.linuxliteos.com/
4. burn the linux installers (which will be .iso files) onto blank dvd's, using a program called infra recorder or imgburn, its good to have them around, you never know when you may need to rescue something. or usb flash drive using a program called unetbootin.
5. go into Windows disk management, shrink the Windows 8 system partition, as you will very likely need Windows for something, someday. make sure you know what the partitions are, shrink the system to a safe usable size. leave the unallocated space alone.
6. you may need to change a bios/setup/UEFI setting, to disable secure boot feature.
7. choose your boot device by pressing F8 or something, it will tell you (briefly).
8. run the system from dvd/flash drive to check temperatures (install psensor), cpu usage, graphics, mouse, external devices etc work, some may need full installation to know..
9. if you proceed to the install wizard of a linux system which is based on ubuntu, then it will usually have the same installer method. when you get to a page of the wizard, showing installation options, choose install to free space, or "something else" for manual partitioning.
for manual, in the unallocated space choose the plus sign to create new partition, this is what you want:
-- swap:
filesystem: linux swap/swap
mount point: no mount point
size: 4-8 gb
-- linux system:
filesystem: ext4
mount point /
size: the rest of the unallocated space you left for linux.
i think thats everything..