Updated by user suggestion. Element added: tzimtzum.
We can’t really understand how the Ribbono shel olam does anything, and so in contemplating the concept of creation we have to fall back on simplifications, models that capture some aspects of the process that we can understand. Traditionally a number of such models have been used; and in fact, the same authority could appeal to more than one. They do not necessarily contradict, they look at the incomprehensible (by man) at different angles and thus match reality in some ways and oversimplify in others.
I thought I would post a survey of some of these models, and I invite the readership to help round it out with anything I may have missed.
1- Manufacture: From this perspective, Hashem first made yeish mei’ayin (ex nihilo, something from nothing) the materials in a step called beri’ah, and then through yetzirah gave them the forms we know today.
2- Speech. The word used in the Torah is “vayomer — and He said”. The world is spoken. As the Baal Shem Tov points out, this is different than writing. Print is written, and then persists without further involvement by the writer. Speech exists as long as the person is speaking. Hashem is still saying the words “yehi or“, since light still exists. Light is in fact the words being spoken.
(Tangent: There is a huge moral implication about the value of words. By this model, you and I are words being “spoken” by the A-lmighty, and thus speech is the essence of our power to create and our very beings. Perhaps this is why dibbur is a word for speech, sharing the same root as “davar” [thing].)
3- Atzilus: Creation is to G-d as light is to a lightbulb. Hashem can choose whether or not to radiate this Light and the how and what should be shined. (In that sense, it’s different than Platonic Emanation, which is a necessary consequence of the Godhead’s existence.)
Atzilus is a model by which such Light shines down from on high, through layers of increasing abstraction until it reaches the physical plane.
The Rambam argues that models #1 and #3, which the Rambam describes as identifying Hashem as Cause vs Agens, are really identical in the Moreh Nevuchim I ch. 69. We also find the Ramban opening his commentary to chumash with the beri’ah – yetzirah perspective of manufacture, but also refer repeatedly to the notion of atzilus and the descent of the Light through veils to lower and lower worlds.
4- Panentheism (not to be confused with pantheism): The idea that the universe is of G-d. He is greater than merely being the universe, but “ein od milvado — nothing exists aside from Him.” The universe isn’t merely made byG-d, or a “radiation” of His G-dhood, but is actually of Him. Based on this model, Chabad teaches that creation is an illusion, an occluding of our ability to see that everything is Him, and thus giving off the appearance that there are multiple existances.
Tzimtzum: This doesn’t merit its own bullet item, because tzimtzum is a feature of either the atzilus or panentheistic models for understanding creation. Tzimtzum is the Divine constriction that makes conceptual room (so to speak) for existence.
The best description I’ve seen for tzimtzum is the metaphor of a slideshow. The projector produces a clear undifferentiated white light. Without the slide, the screen is simply white, with nothing existing on it. The presence of people, buildings, or whatever on the screen is due to the slide selectively blocking light from reaching the screen.
But obviously tzimtzum is metaphoric. As is clear from my circumlocution of “conceptual room (so to speak)”, no one is suggestion that Hashem actually constricts Himself. That would be suggesting a change in an unchanging G-d, and a reduction of His Absolute infinity. Neither idea is consistent with Yahadus.
So the question becomes interpreting the metaphor, given that we can only understand a glimmer of what it’s a metaphor for. And this becomes the basis of the distinction between the atzilus and panentheism models. The first approach is that what was constricted was not the Ein Sof (the Absolute Infinite) Himself, but the Light which is ne’etzal from Him. The “veils” that occlude some of the Divine Light are like the slide in the slide projector metaphor. The second is that we’re speaking of the Ein Sof, but it’s only an illusion — in reality, everything is G-d, but we are given the illusion of things existing as distinct from Himself.