This requires creating a separate home partition when partitioning the disk and mounting at /home. If you want to move the user's current home directory within the root filesystem, you can use this command while logged in as root/another user (don't do this if you're logged in as the user you're moving).
# usermod --move-home --home /newhome/username username
Some distributions (like debian) offer to do this for you automatically at install.