Our main sources of information about the Hanging Gardens are ancient descriptions. As a result of those descriptions, archaeologists know roughly what they're looking for at Babylon, and art historians know roughly what they hope to find in Mesopotamian art. In addition, we have a few important early references to them, and some archaeological work has also been done. So we have four types of sources:
In essence, everything depends on those descriptions.
So it is essential to treat them right, to know their dates and their authors, to know their authors' reasons for writing and what those authors understood by "truth", and to know whether the surviving documentation has transcribed them in a way we would consider accurate today.
That is a lot to keep track of, and the key is organization.