What do they need to do to determine what time period Eocene belongs to on the geologic time scale

They need to scan a chart on the internet and you know when you find it.

There are certain steps taken by the professionals in order to know more about a certain civilization inside the history of man kind, as there archaeologist and other research workers who digs deep inside the ground and explores the different artifacts which are possibly there to be analyzed by the professionals and then the prepare the different documentations to keep a record of each civilization that existed in a certain period of the planets history.

But, it is not that easy as it seems because there are a lot of techniques and standards that are involved in the whole process, as there may be presence of a unique architectural sites, ancient dress and artifacts etc which are studied by a team of professionals and then the standard is there to analyze each and every thing relating the items in the area. So, after an extensive process by the professional a valid conclusion is concluded by the team of professionals.