1) Taken your question literally: One does not need to argue that consciousness exists. Everybody when awake is conscious and experiences consciousness.
One can discuss whether every perception is a conscious perception. Because we know that humans can also be triggered by unconscious stimuli. This kind of stimulation is used by marketing mechanisms or by priming, applied in an experimental context of cognitive psychology.
2) Hence the question is not, whether consciousness exists. The questions are:
How to define conscious mental processes and how to establish the border to unconscious processes?
Why are some mental processes conscious while others are not? What is the function of conscious processes?
As an introduction I recommend Koch, Christof: Consciousness - Confessions of a Romantic Reductionist. (2012). Chapter III reviews some definitions of conscious processes, taken from different view points.
Whether a person is conscious or not and to which degree he is conscious can be derived from its behaviour. That’s a method used by paramedics using a checklist.
A more refined criterion to decide about the conscious state of a person is to check the activity of the neocortex and the thalamus.
A more philosophical definition of being conscious is to register how things seem to us (qualia).
In any case, conscious mental processes are restricted to the neocortex.
3) An early classification of states of consciousness is given by the Mandukya Upanishad from the beginning of the common era. The Mandukya Upanishad distinguishes four quarters of atman (= the self):
Vaisvanara: “situated in the waking state, perceiving what is outside […]” (verse 3)
Taijasa: “situated in the state of dream, perceiving what is inside […]” (verse 4)
Prajna: “situated in the state of sleep – deep sleep is when a sleeping man entains no desires or sees no dreams […]” (verse 5)
“They consider the fourth quarter as perceiving neither what is inside nor what is outside, not even both together; not as a mass of perperceptions […]” (verse 7)