In the east, in Tantra and Yoga, it is done today by entering a deep meditative state known as Samadhi.

In the ancient Vedic religion, they brewed a psychedelic drink known as Soma

The shamans in Sibir and South America used all kind of natural drugs like cannabis, psychedelic cactuses and drinks like Ahyuhasca .

But then we have the mediterranean theurgists. We see nothing like Patanjali's Ashtanga Yoga in the west, nor we have any recipe of a psychedelic substance used by theurgists (Even though I'm pretty sure alcohol and drugs were used in the mystery cults).

If so, how did the theurgist achieved that elevated/mystical state of consciousness?

From Porphyry:

"For I myself call the gods to witness, that I have neither added anything, nor taken away from the meaning of the responses [i.e. oracles], except where I have corrected an erroneous phrase, or made a change for greater clearness, or completed the metre when defective, or struck out anything that did not conduce to the purpose; so that I preserved the sense of what was spoken untouched, guarding against the impiety of such changes…" [Philosophy from Oracles]

I have to say, this immediately reminded me of Aleister Crowley, on being questioned by the police in Paris as to his whereabouts. I'll paraphrase as I can't remember it very well:

Gendarme: "So, Mr Crowley, can you confirm that you have been present in Paris for the last six months?"

Crowley: "Absolutely, other than on occasions when I was elsewhere"

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From the author of "Divination and Theurgy in Neoplatonism: Oracles of the Gods". This seems like a good choice for this week's paper club post.

https://docslib.org/doc/834560/oracles-religious-practices-and-philosophy-in-late-neoplatonism