Tails does not require, and actively avoids using, HDDs or SSDs as it is intended only to be used with removable media to avoid leaving traces that it was ever run on the computer. It should operate fine from being installed on a USB or DVD without any other storage media attached.
From the Tails website:
Tails is configured with special care to not use the computer's hard-disks, even if there is some swap space on them. The only storage space used by Tails is in RAM, which is automatically erased when the computer shuts down. So you won't leave any trace on the computer either of the Tails system itself or what you used it for. That's why we call Tails "amnesic".
To create a Tails USB or DVD, you should simply be able to follow the steps outline by the Tails Installation Assistant.
A crash course on "Tails for journalists" available from Infosec Bytes help you familiarise yourself with the concepts behind Tails and of course there is Tails' own extensive support documentation and design documents.