The correct term for "splitting up" a hard drive is called partitioning. That may help you if you try to google for guides on what to do.
dgingeri's suggestion to use a VM is a pretty good one because it saves you from many of the hassles involved in using Linux... like finding certain drivers.
However, to answer your question "as-is", you would need to: (1) shrink the partition on your HDD, (2) create new Linux partitions in the blank space, and (3) install Linux in the new partitions. Nearly all Linux distributions come with partitioning software that can do this for you as you're installing them. Some tips for that, (1) make sure that if given a choice, you "manually" partition so that Linux doesn't try to install on your SSD instead, and (2) when asked, your should install the bootloader either to the SSD *drive* for a BIOS install or to the UEFI *partition* on the SSD drive for a UEFI install. You can usually tell whether Windows was installed as BIOS or UEFI during your Linux install because Linux should detect whether a UEFI partition exists or not. Make sure you find a guide for your distribution if this is all unfamiliar to you, but what you're doing is pretty common so it's not difficult to find help.
In my experience, you don't actually have to repair Windows unless the partition you are changing is the Windows system partition (the one on your SSD). So that probably won't be an issue for you.