One has to read The Critique of Judgement in the full context of Kant's philosophy, especially his Critique of Pure Reason, to fully understand how he made modern art possible. To Kant, the world we observe with our senses is not an independent reality that interacts with our means of awareness, thus giving us the awareness of objects out there. Instead, he came up with what he called his "Copernican Revolution" * whereby he reversed this process. To Kant, there may be a real world out there (the noumena), but we are not directly aware of it with our senses. He claimed that somehow the noumena interacts with our mind # and that which we observe is a subjective projection (the phenomena) not directly dependent on the means of awareness (our senses). Thus, the world we observe does not resemble the real world at all -- it is just a projection of our mind.
Keep in mind that to Kant, the apple we observe is not the real thing in reality, the real thing in reality (the noumena) interacts with the human mind and via the sensory manifold projects the image / form of the apple, which has no resemblance to the apple-in-itself (the real noumenal apple). In fact, because we have not thoroughly analyzed how this all works, we cannot even be sure there is a apple-in-itself leading to the projection -- it might be a mental burp of some sort. So, a painting of an apple (the formal apple, what we observe) is not a painting of the apple (the noumenal apple, the object). In effect, this means that anything goes, so long as one does not make art in the image of that which we observe, since this isn't reality in the first place; and who is to say that someone else's subjective projection is not radically different from our own? Maybe those empty smears on canvas is how they experience reality as they seek to get closer to the truth by not focusing on those projections of the mind.
* [From Kant's introduction to his Critique of Pure Reason]
"Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our knowledge of objects by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge. This would agree better with what is desired, namely, that it should be possible to have knowledge of objects a priori, determining something in regard to them prior to their being given. We should then be proceeding precisely on the lines of Copernicus' primary hypothesis. Failing of satisfactory progress in explaining the movements of the heavenly bodies on the supposition that they all revolved round the spectator, he tried whether he might not have better success if he made the spectator to revolve and the stars to remain at rest. A similar experiment can be tried in metaphysics, as regards the intuition of objects."
# The reason I have to say "somehow" instead of causally interacting with our senses is that Kant held that causality was an affectation of the human mind, and not a metaphysical principle based upon the nature of reality. In other words, given his "Copernican Revolution" stated above, the human mind creates the structure of what we usually refer to as reality -- the "order" of the universe and the observation of consistency in existence. It's not that the human mind did anything to the Noumena out there, but rather what the human mind did to its interaction of the noumena with our modes of awareness -- leading to an orderly universe that we project inside the human mind. For a better understanding of causation or causality, see my essays on the topic.
[added 02/29/2012 as an overview of my position: To Kant, that which we observe is not existence, but rather the phenomena, and it is dependent on human consciousness (see his "Copernican Revolution" stated above). Hence, that which we observe is not the real reality, but only the reality that conforms to our mind (our innate structures of the mind, such as causality, logic, form). To Plato, the real reality was the world of the Forms, which he held were static, and we only get motion or change due to the fact that the Forms didn't interact with matter very well. To Kant, the real reality is formless (chaotic, random, unknowable), due to the fact that our minds conform (the noumena to) the reality that we observe. Real reality, according to Kant, would be formless and not immediately graspable to the human mind. And we do not get real reality via sense perception. The only way to comprehend real reality is to use Pure Reason -- reason not derived or dependent upon perception or that which we observe. Since it is this Pure Reason that conforms the reality that we observe, he held that the only way to grasp reality the way it really is was to disconnect the mind from the perceptually self-evident, and use Pure Reason. If we could understand the structure of Pure Reason, we might be able to figure out what the human mind does to the noumena and maybe have some grasp of reality the way it really is, but he held that this was impossible, since we are confined to awareness using human apparati (the sensory manifold) and Pure Reason, which is still dependent on being human.
With this view of existence and our awareness of it, the rejection of art that presents the perceptually self-evident is naturally and logically rejected as having nothing to say about reality the way it really is (apart from human awareness and human distortions). Hence, briefly, this leads to art which is an offense to the imagination, as Kant held in his Critique of Judgement -- art that is not a depiction of the forms we observe with our senses, but rather a rejection of such forms in order to get to real reality, which we can only know by divining the structures of the mind.
His whole philosophy is really a form of subjectivism; saying reality (the phenomena we observe) is dependent on human consciousness for it's form and consistency. And it is only by rejecting this, that we can come to grasp existence the way it really is.]
I'm not going to do a full-scale proof that Immanuel Kant laid the groundwork for modern art, but the following essays give a good indication of how he led to non-objective art (art not concerned with the object of observation).
For those who assert that Kant did not create Dadaism and Cubism and Surrealism or other modern art movements, this may be correct in terms of specific aestheticians coming out and creating those specific movements. However, they are accepting Kant's basic premise of that which we observe with the senses is not real reality, and therefore anything goes so long as it is an offense to the senses. Besides, it is often the case that a certain philosophy will spread through intermediaries who will draw out the implications in a logical manner. This happened with Plato leading to the Dark Ages and Aristotle leading to The Enlightenment. It's not that Augustine was a Platonist (though one can make the case that he was a neo-Platonist), but rather that he took the fundamental approach to truth that Plato had (of ideas divorced from the perceptually self-evident) and making claims about existence and what is really real and what isn't. Plato was unaware of the Christian God, but Augustine incorporated Platonism with Christianity, leading to the Dark Ages. Similarly with Aristotle and the Age of Enlightenment, which came about through Aquinas and those who followed him, which was a new understanding of the objective approach (of understanding existence via the perceptually self-evident). Unfortunately, Aristotle was not the complete answer, and so it was open to skepticism, primarily through his theory of how man gains abstractions, and so a Kant could come along and blast it all based on that skepticism, and turn it all on its head. The point is that if one is going to accept the idea that the reality that we observe is a projection of the mind (Kant's "Copernican Revolution"), then it doesn't have to be taken seriously, even in art. So a painting of an apple is just trite according to Kant's followers, but empty smears on canvas is profound (precisely because it is not based on the perceptually self-evident).
Now, what is the difference between Kant and Ayn Rand in general and as these ideas relate to art?
Kant held that our perceptual experience of existence is mere subjective and stems from a priori ideas (innate ideas, ideas prior to experience and thinking) making our experience of existence mere subjective (stemming from the subject, the observer). In order to experience something beautiful in observation, like a sunset, Kant held that we have a prior aesthetical ideas that govern what we experience. He held that due to the fact that we can communicate the sunset with others that there is a type of universal subjectivity, but that matters of aesthetics is really just a subjective experience. Hence there is no objective criteria for that which is beautiful (objective here meaning apart from the subject, something from reality per se). Since there is no objective criteria for beauty as such in nature, then there is no objective criteria for things made by man, such as art. Hence, anything goes so long as the artist can claim to be objective apart from what we observe. That is, so long as the supposed artist is presenting something other than that which we observe, he can claim objectivity regarding his supposed artwork.
Ayn Rand is totally different. There are no a priori ideas. Man is born tabula rasa and has no innate ideas and one's ideas do not govern that which one observes. What we observe is not a subjective experience, but rather is objective, meaning that while it is true that we can see red because we have eyes and neurological optical pathways of a specific type, this does not make vision a subjective experience and what one observes is not conditioned or based upon a priori ideas. We observe that which exists and our experience of existence is objective precisely because we have the type of body that we have and are aware of existence via sense perception. Our ideas stem from or are created from thinking about that which we observe (there are no a priori ideas already there prior to experience). Hence, an objective idea is one that is based upon that which we observe, based upon existence, so long as one follows a rational epistemology -- based on the facts of reality in an mentally organized fashion based upon the observation of similarities. This gives rise to objective ideas in all areas of life, including art. She outlined her objective criteria for art in her The Romantic Manifesto and demonstrated her means of creating art in her novels. The primary purpose of art is to bring ideas down to the perceptually self-evident -- in other words, to give factual evidence for the idea in material form (i.e. say a painting or a statue or a novel), which means that art must conform to both existence and the nature of human consciousness to be objective.
For an artistic representation of the modernization of so-called art, I recommend this image.