That's fascinating to this lay clay tablet thinker. It had never occurred to me that clay tablets were reused. In fact, it nearly fundamentally changes my estimation of them as a long-term durable storage medium.
Hardening clay is relatively simple (just as any other pottery) but optional - you can choose to keep the clay unbaked if you want to reuse it (it would dry out but can be made wet again), but you can also make them permanent.