At least some distros offer shrinking NTFS partitions during the Linux installation. Of course, this is possible with free space in that partition only. And you should run Windows' check disk tool immediately before.
There is always a risk when playing with file system structures and partition tables (you should "try" not to have a power outage then...) but this risk is rather low. Nonetheless: Assess the possible damage and make a backup in case of doubt. You should at least copy the most important data to
After shrinking the Windows partition one or more additional partitions are created. 10 GiB is enough for Linux itself. The demand for your $HOME space is quite different from user to user. Maybe you want to store most of your data on the NTFS partition for a while and thus need only little space on the Linux file systems.
It is (or was?) even possible to install Linux into a Windows file system but that is no fun.