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The Windows Disk Management Utility
My first step is to create some free space on the disk drive. Most of the major Linux installers are able to do this automatically if you let them, but I am a bit of a control freak (or a bit paranoid, depending on how you look at it), so I prefer to set up the disk exactly the way I want it in advance.
The most obvious way to free up some space is to reduce the size of the Windows C: partition. To do that, I could have used either the Windows Disk Management utility, or one of the Linux disk/partition manager programs such as gparted which I will show later as a typical example for Linux.
The Windows 8 Disk Management program can be reached through Control Panel / System and Security / Create and Format Hard Disk Partitions.
The display will be as shown above, but with the Windows C: partition filling all of the space between the EFI Boot partition and the Recovery partition.
I selected the C: partition by clicking on it in the partition list or in the graphic partition display, then went to the menu bar and choose Action / All Tasks / Shrink Volume. The program will take a bit of time to figure out how much it can shrink (this has something to do with "unmoveable files"), and it will then let you either accept the maximum shrink, or select some smaller value.
It will then take just a few minutes to actually shrink the partition, and the display will end up looking like the one above.