The culture that Enheduanna was born into is the very same civilization that invented writing. Everything from sales receipts for cows, to sacred writings and temple hymns, were written in the unique form of cuneiform.
While there were carvings made on giant temple walls, and large stone-like structures items carrying cuneiform writings, there were also small clay tablets used for writing.
A scribe would use a small tablet of wet clay, inscribe the cuneiform into the clay with a reed, and then either let it dry or bake it dry.
The power of cuneiform is that it seems to last forever and it has allowed us insight into Enheduanna's life and work, as well as providing insight into a great deal of ancient history.