Let's say for example a guy with the name Robert has won one of the grail wars. Can he wish for omnipotence, or does he need to know a method on how to become omnipotent?
In a way I believe they could have such a wish granted.
The Swirl of the Root (根源の渦, Kongen no Uzu, "the Vortex of Radix" in the English localization), also known as the Akashic Records, the Spiral of Origin or the Root (根源, Kongen, "Radix" in the English localization), is a metaphysical location within the Nasuverse that acts as the "force" that exists at the top of all theories in every dimension, as well as the source of all events and phenomena in the universe. It is also referred to as the "Outside of the World," as opposed to the World and the Reverse Side of the World. Existing outside of time, it stores and archives information of all possibilities and events, past, present, and future, of the world. It is the place from where all souls, including those of Heroic Spirits recorded on the Throne of Heroes, originate from and to where they return after death.
For a Magus like Tokiomi Tohsaka whose desire to enter the Holy Grail War was to use the Holy Grail to reach The Root they may become omnipotent because of what they can do with it by what is claimed by Shiki Ryougi's third personality 「 」 (AKA Void)
She claims restructuring the laws governing atomic matter, going back in time to change the evolution and development of all life, and reconstructing the orders and laws of the world would be easy for her to accomplish. It is not actually changing the existing world, but instead annihilating the old one with a new reality.
Despite this ability, her combat ability is only possibly around the level of Ciel, allowing her to manage a defensive fight against a being on the level of a Servant. She is still much stronger than the regular Shiki [Tohno Shiki], who holds no hope in even competing with a Servant defensively.
However, she was later noted to be the second strongest being in the Nasuverse when not including Servants, under Arcueid Brunestud and above Primordial Demons.
Kischur Zelretch Schweinorg and Aoko Aozaki who both wield True Magic (2nd and 5th respectfully) have already reached The Root to gain their True Magic and while Aoko's 5th Magic's domain is uncertain, Zelretch's 2nd Magic is the Operation of Parallel Worlds which also also includes time travel while the 3rd Magic Heaven's Feel, the whole point of the Fuyuki Holy Grail Wars that the Einzbern seek to reclaim, is the Materialization of the soul.
Given that the subject Holy Grail in Fate/Apocrypha is the Fuyuki Holy Grail I would assume the same functionality.
Knowing how to become omnipotent however I don't think is needed because it was Angra Mainyu saying it was how it would grant Kiritsugu's wish as if Angra Mainyu was going to use the Grail for Kiritsugu.
One of the things about the Holy Grail in Fuyuki which is also mentioned by Rin in Fate/Stay Night is that only a Servant can use the Holy Grail which is why a Master who can contract another Servant after theirs are defeated is still a participant in the War than one who can't.
At the time there was also a serious flaw in this system, As the Grail required the energy of all seven Servants to help activate the Great Grail and open a hole to Akasha, it would mean that all Servants including the victor Servant would have to be killed, and since the Grail can only be held by Servant, activating the Greater Grail, let alone retrieving the Holy Grail, cannot be achieved, as Masters are incapable of doing so without a Servant. This flaw made the Grail capable of only granting wishes to Masters and Servants.
Source: Fuyuki Holy Grail War
As Angra Mainyu is formally the Avenger Servant it makes sense that Angra Mainyu could operate the Grail in place of Saber and Kiritsugu's "corrupted" wish is just Angra Mainyu's own understanding of how it would make such a wish believing that Kiritsugu's current methods aren't inefficient but the correct way.
Tokiomi and more than likely any other Master planning to use the Grail to reach the Root would plan to have keep one Command Spell so make the Servant commit suicide. For wish granting a Master would probably keep a Command Spell to force the Servant to grant their wish rather than the Servant's wish unless there was an understanding for the Servant's wish to be granted in another way (ie. Diarmuid Ua Duibhne's wish to have a Lord to serve was granted by meanly being summoned).
In Fate/Extra the Holy Grail is the Moon Cell and the right to use it
In the Fate/Extra universe, the Moon Cell (ムーンセル, Mūn Seru?), also called the Holy Grail, Eye of God, and Divine Automatic Recording Device, is a massive collection of photonic crystals within the moon that comprises a giant supercomputer of sorts.
It is a processor with a massive memory that has recorded the habits, history, ideas, and even the souls of humanity. As it can also affect the outside world with its calculations, it has the power to "grant wishes." In this way, it can be thought of as a Pandora’s Box that promises the next stage of evolution. It promises god-like power to those intelligent lifeforms who have become technologically advanced enough to scan the interior of the moon.
Source: Moon - Moon Cell
So while it's not exactly like the Fuyuki Grail or what Void claims to be able to do you can still alter the world but it'll just take a bit of time, an example cited in Fate/EXTRA material - Encyclopedia: Holy Grail [Circumstances], page 194
You might say “I want all the girlies in the world to be mah little sister" for example, and then in about ten years, it would be assumed that society on Earth would be reorganized in that fashion.
Of course not sure this is really being omnipoten
However like the Fuyuki Holy Grail there is something in the way and that's Twice H. Pieceman who was a self aware NPC who won the Holy Grail War, however because of checks within the Moon Cell Twice can't use it as a NPC would be deleted so he would ask later winners of the Holy Grail War to make his wish for him, refusal would be met with them being destroyed by him and Savior
However, once he reached the core of the Moon Cell, he found that, as an NPC, he could not enter the core without being deleted as invalid data. From there, he redesigned the Holy Grail War to the current system and asked each Master who was victorious in the Holy Grail War to wish for the perpetuation of war and the continued advancement of man. However, all the Masters who faced him refused, and thus were killed by him and Saver.