My personal preference for installing a new tinycore system to a hard drive is to use "usbinstall", available from the control panel, although others may disagree.
You will need to install dosfstools and syslinux via app browser first before running usbinstall. A copy of the tinycore iso is also required (unless you point usbinstall to the "running" system which might be more complicated for a new user). When asked about a drive, type in hda, and when asked about what type (ext, hdd, or zip), read the description and choose which is best for you. I usually choose ext (ymmv)
good luck
3rail