Here's a Mint tutorial you might want to have a look at:
[TUTORIAL] Installing Mint on a Windows 8/8.1 Computer
. You can apply most of the info there to other distros.
It's geared toward Linux newbies, so gloss over the basics you already know if you're not new to Linux. Pay particular attention to the "Preparing Windows for the Linux Installation" section. In addition to things there, booting your Linux install disk
(Mint or other distro) in the same mode that Windows was installed in is the key.
You'll need to refer to your computer's user manual for instructions on changing the UEFI settings for that. They differ from manufacturer to manufacturer.
Also, if installing in UEFI-mode (most likely), grub bootloader gets installed to the EFI System Partition, not the MBR.
Near bottom of tutorial are links to more info on UEFI, Disabling Secure Boot and Fast Startup, etc.
P.s. If you do have a system where Windows 8 is installed in Legacy-mode, then ignore those instructions. Just make sure the Installer disk gets booted in Legacy-mode too, then proceed as if it were any other run-of-the-mill Linux install.
P.s.s. Not sure how many Linux distros support secure booting as of yet. Ubuntu does, but don't think Mint does. Not sure about any others, but possibly Suse & Fedora might as well. Check the distro's site for details on that if it's important to you.