Okay I can do this but what period are you asking about are you asking about the Hermes Trismegistus created during the Hellenistic period?

If so it was a combination of both the rituals of the Egyptian practices relating to the God Thoth and the Greek god Hermes. They were worshiped in the same temple and according to the writings of Amenohtep and Teos they were both considered gods of magic and writing.

Later according to stone tablets that were discovered that were dated to the Mycenean period they were combined into a single Deity. However it's a bit of a... how to explain accurately..

I'd say not everyone agrees on the translation as parts are damaged on the name they become known as the thrice blessed deity or triple Hero .

The central " Tenants" at this period are "Word magic" spells were written on scrolls rather than said at least according to the aforementioned two "writers"

However an invocation translated from Khor Kosmu is as follows

Such was all-knowing Tahuti [Thoth], who saw all things, and seeing understood, and understanding has the power to disclose and to give explanation. For what he knew, he graved on stone; Yet though he graved them onto stone he hid them mostly... The sacred symbols of the cosmic elements he hid away hard by the secrets of Osms ... keeping sure silence, that every younger age of cosmic time might seek for them.

Now my knowledge of the Greek parts of the texts are quite poor so I can only offer this

Sources

SR Meade translation of the temple writings in Khmunu

The translation of the writings of Amenohtep found in. Thoth or the Hermes of Egypt: A Study of Some Aspects of Theological Thought in Ancient Egypt',p.166-168, Patrick Boylan,Oxford University Press, 1922.

Don't take this amiss, but this doesn't read like a historical question. The way this is worded, it sounds like you're asking about the actual, mechanical practices of the Art and the organizations that practice/have practiced it. That's entirely outside the scope of this sub. If you're interested in the history of hermetic magickal traditions (the Golden Dawn, for instance), and potentially how their practices differed, then you're in the right place. (Though I don't know if anyone here is truly qualified to answer—I haven't seen anyone with a History of Magickal Traditions and Practices flair.)

If it is the mechanical workings that you're after, then you're going to have to go to the primary sources (and all that the word "primary" implies). Aleister Crowley is the classic, of course, but Israel Regardie is probably also a good place to start.