Through reading books on Buddhism I get the idea that existence is conditioned. The faculties (mind, consciousness, etc.) through which we try to attain Nirvana are also conditioned. So, how is it possible to attain the Unconditioned through conditioned faculties?
Nirvana is a non-affirming negation. Uncompounded space is a great example of something that exists (ie., it can be known) and is also a non-affirming negation and is a helpful illustration.
There are two different concepts that are often labeled by the word "space" and get confused together:
Compounded space is the vacuum between material things. Take two material objects (made of matter) that are space-like separated. This means not only that they don't occupy the same space, but that they have a vacuity between them. Imagine they are placed in the void of deep space with a meter of distance between them. In this meter of distance between them, there is no air, there are no molecules, no matter. There is only void. A meter's worth of void in fact. This is what is meant by compounded space.
Uncompounded space is the complete absence of obstructive contact. It is not the same as the void above, but rather the absence of obstructive contact that the void sits in if you will. It is the space (the utter lack of obstructive contact) that remains whether something is occupying it or not. As was described in another answer (a great analogy!) imagine a building that is scheduled to be demolished. The space that it is sitting in while it exists and still remains after it is destroyed - that is what is meant by uncompounded space. It is a mere lack of obstructive contact.
Can you visualize and understand what is meant by the above two descriptions? Can you see how they are not the same thing? The latter definition is not describing a conditioned thing. Rather, it is a non-affirming negation. Nirvana is also an existent (ie., it can be known) that is a non-affirming negation and thus said to be "unconditioned."
Here is a link to a text that explains this by a Tibetan Buddhist Gelug master:
The suttas also say (eg. MN 44) the Noble Eightfold Path is conditioned (fabricated).
Imagine Nibbana is like space and you want to create space by removing a building. The building is conditioned and the demolition explosives are conditioned. But the space that remains after the building is demolished by explosives is unconditioned because the space has always been there.
(Note: In Buddhism, space is not unconditioned. The above is merely a close analogy).
Similarly, the peace of Nibbana is always there, forever. It is unconditioned. But the conditioned Path is required to remove the conditioned defilements that block the experience of the peace of Nibbana.
I think that most traditions would say that Nirvana (or Nibbana in Pali) is not created. People wouldn't say, "I'm doing Nirvana" either. It can't be defined by words in the sense that you can give the words to someone else and they can make Nirvana by following or understanding the words. Some would even object to saying it is "realized".
My favorite description of it has to do with release:
Disenchanted, he becomes dispassionate. Through dispassion, he is fully released. With full release, there is the knowledge, 'Fully released.' He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world. link
In this statement, "there is knowledge" is the way it is described. Knowledge of how stress is created, how it is released, how to see the world without clinging/stress/dukkha.
Just like knowledge isn't created, Nirvana isn't created. But there is a path to knowledge. And all traditions have a path. For some, it is the Eightfold Noble Path. For others it may be Zazen. Or Tantric practices.
Different traditions have somewhat different characterizations. (The wikipedia article on Nirvana is not bad). But, I think all traditions will characterize greed, aversion/anger, and self-identity as things that dissolve with Nirvana.
It is confusing to read about Nirvana in different traditions, because traditions have conflicts in the details. So, if you mix and match, you'll get confused quickly trying to make them make sense. I'm in the Theravada tradition and this book is a single tradition take on it. https://amaravati.org/dhamma-books/the-island/
(even within one tradition, you'll still have disagreements.)
In Buddhism, Conditional and Unconditional are discussed in context of dukkha vs peace. Dukkha is a painful feeling of wrongness, arising whenever there's a clash between your expectation and your actual experience. Peace is experienced when there's no such clash.
Now, when you cling, you cling to Conditional, therefore your peace gets conditional. When the condition you cling to is satisfied, there's no clash, so you have peace. You only have peace if your condition is satisfied.
When you cling to judgments, concepts, categories, philosophical views, ideas of how things should be, comfort, fairness, spirituality, your sense of identity (both personal and group identity), all kinds of abstractions, not to mention clinging to the state of material things in your life wishing it to never change - in all these examples you setup dependency on a condition.
Even when you cling to a peaceful state of mind, right there is a dependency on condition.
When you don't cling, you don't depend on Conditional, therefore your peace is Unconditional. Whatever happens, you are at peace. You are at peace because there's no clash, because you don't cling to any fixed idea how things are supposed to be.
So when you lose a fixed shape, stop grasping at a certain identity made of concepts, when your position cannot be pinpointed, when you don't cling to either the material nor to the mental states - then there's no longer anything rigid that would be a subject to conditions.
Then that's a different kind of peace, not the regular peace conditioned on e.g. silence, but the unconditional Super-Peace. Whether you are sitting in meditation or your house is full of crying babies that you have to console, this Super-Peace is not lost. What could death do to it if there's no grasping to anything that dies?
That's the Unconditional. As we say in Mahayana, in a sense you had it even before you started looking for it and indeed before you were born, but it does take some work to rediscover. When you "attain" it, you don't really attain anything at all. This is why it's called Anuttara Samyak Sambodhi - unexcelled most perfect enlightenment.
Faculties (mind, consciousness, etc.) through which we try to attain Nirvana are conditioned. How is it possible to attain the Unconditional through Conditional faculties?
Now you can understand this answer: we don't "attain the Unconditional through Conditional faculties". If we keep on clinging to faculties, to any form of mind, consciousness etc., we keep remaining subject to conditions.
How is Nirvana possible if everything is conditioned?
It is possible because the conditions in and of themselves are not the cause of dukkha. The cause of dukkha is a mismatch between expectations and experience. So even though the experience is conditioned, if you don't cling to expectations there will be no dukkha. That dukkha-less Super-Peace is what we refer to as the Deathless, the Unconditional, Nirvana.
The burning of a fire produces flames, it is dependent on fuel & supportive conditions, burning is conditioned. The extinguishment of flames depends on the exhaustion of fuel and requisite conditions for burning. We can say that the cessation is conditioned by the process of burning and exhaustion of fuel.
However extinguishment is not a thing among things there; it is not the fuel, it is not the flame, it isn't the perception of burning, it is not the heat.
It is like the end of a story, there are events leading up to it but the end in and of itself is not part of the narrative, it is not something that is experienced by a character in the story, it is not an event occuring for this or that personage and like extinguishment is not a thing among the things that are extinguished or said to end.
Therefore when we talk about the principal extinguishment of the conditioned, the extinguishment principal is then by definition unconditioned because it is not a thing among the conditioned things that are there extinguished.
The cessation of a flame is a truth to be observed & known as the non-occurence of burning. The cessation of the conditioned is a truth to be observed & known as the non-occurence of the conditioned or that which changes as it persists.
Just like the extinguishment of a flame is not a thing among the things that are said to be extinguished, so is the extinguishment principle of the conditioned is not among the conditioned things.
The name of a person is neither his mind nor his body, here analogically the semantics of our understanding are such that name of a thing is not found among the things that are named.
subtle impermanence is the absence of a moment of a thing being able to endure into the next moment thru its own volition. in other words death is unproduced/unconditioned as its already a feature of a moments birth/production.
similarly nirvana is the absence of mental affliction enduring as the nature of awareness. complete freedom of the mind is uncaused since its already a feature of mind capable of recognition.
I think it's to do with absence.
For example -- a simple though perhaps not very deep analogy -- you might as well equally ask, "How is it possible to hear silence, when ears hear noise or sound, and silence is an absence of sound?"
The Brahmana Sutta (SN 51.15) suggests it's a case of, "Having arrived, the corresponding desire/energy/idea is faded away."
A way in which one arrives is described in SN 41.5:
Greed, hate, and delusion are bonds. A mendicant who has ended the defilements has given these up, cut them off at the root, made them like a palm stump, and obliterated them, so they are unable to arise in the future. That’s why a mendicant who has ended the defilements is called ‘unbound’ ('abandhana').
Training yourself not to get angry and so on, to do away with the habits and thought processes and attitudes from which anger arises (see also What is effluent?) -- that seems to me do-able even if not everybody does it, I don't see why it should be theoretically or logically impossible -- and see plenty of people, especially adults, perhaps it's even the norm, that people appear to be at least partially successful.
One more thing, consider doing something wrong as the result of certain conditions. Conversely if you don't do something wrong, then that (non-existent) action isn't conditioned, its non-existence isn't impermanent.
AN 4.159 below explains this very topic and it's quite self-explanatory.
Then Ven. Ananda approached the nun and, on arrival, sat down on a prepared seat. As he was sitting there, he said to the nun: "This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.
"This body comes into being through craving. And yet it is by relying on craving that craving is to be abandoned.
"This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.
"This body comes into being through sexual intercourse. Sexual intercourse is to be abandoned. With regard to sexual intercourse, the Buddha declares the cutting off of the bridge.
"'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival & continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, & live in comfort.' Then he eventually abandons food, having relied on food. 'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said, and in reference to this was it said.
"'This body comes into being through craving. And yet it is by relying on craving that craving is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk hears, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered & remains in the fermentation-free awareness-release & discernment-release, having known & realized them for himself in the here & now.' The thought occurs to him, 'I hope that I, too, will — through the ending of the fermentations — enter & remain in the fermentation-free awareness-release & discernment-release, having known & realized them for myself in the here & now.' Then he eventually abandons craving, having relied on craving. 'This body comes into being through craving. And yet it is by relying on craving that craving is to be abandoned.' Thus was it said. And in reference to this was it said.
"'This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk hears, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered & remains in the fermentation-free awareness-release & discernment-release, having known & realized them for himself in the here & now.' The thought occurs to him, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered & remains in the fermentation-free awareness-release & discernment-release, having known & realized them for himself in the here & now. Then why not me?' Then he eventually abandons conceit, having relied on conceit. 'This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.' Thus was it said, and in reference to this was it said.
"This body comes into being through sexual intercourse. Sexual intercourse is to be abandoned. With regard to sexual intercourse, the Buddha declares the cutting off of the bridge."