Wat are some of the things archaeologists study to gather information about early agrarian societies are

Remnants of old tools, whether they be crude stone or remaining biological matter.  The biological matter can be carbon dated, and many of the items have ended up in strata that also define their dates.

As to other information, fire construction, cave paintings, and other artifacts can illuminate many items about an early agrarian civilization.

Finally, the selective breeding of a plant can determine many what's and why's of a society.  Just as one example, the orange was originally a fruit mentioned in Chinese writings before BC became AD.  It is a bred species.