There are many ways to point to non-duality. The traditional vedantic method is called the “Arundhati darsana nyaya” or “the logic of viewing arundhati.” The context being, arundhati and vashishta are two stellar constellations which are considered to be a pair when observed anstronomically, but arundhati is much farther away than vashishta, and so is very faint in the night sky. The way a teacher might show a student where arundhati is in the night sky might be to follow a sequence of referential pointers. He might draw the student’s attention to a specific tree, and then a specific branch of the tree, and then a bright star that is visible above the branch, and then a fainter star beyond it, and then in its vicinity a fainter star still - which is arundhati. The logic being, the student will not have a frame of reference to detect the very subtly illuminated arundhati when directly pointed to. By going through the sequence of referential pointers, their attention is gradually drawn to it, until it becomes apparent what/where it is in the vast night sky.   when non-duality is taught, it is often  taught after a certain degree of stillness has been attained by the student - they go through preparatory practices such as yoga, breath work, meditation to attain onepointedness of the mind. Once the mind has been developed sufficiently, the teacher will draw the student’s attention to their witness state - which observes all phenomena occurring but is itself unaffected by the phenomena. The mind itself is an object to this witness awareness. At this point there is a separate reality that is being observed by the witness, so there is duality. But the duality is clearly partitioned into subject and objects. 
  The student stays in this way for a while until the thought arises in their mind, this still is duality, and so asks the teacher exactly how is this nonduality?   The teacher then helps the student realize that the world that is observed is just a series of thought patterns appearing in the student’s mind. So the “world” doesn’t really have a separate existent reality apart from the mind. But since the mind itself is an object to the witnessing awareness, it too much be an appearance, much like the world. 
  The student sits with this new insight and meditates on it - until one day the realization dawns - the only reality that is unchanging is the witness awareness. This awareness has no attributes other than existence and knowing (sat and chit). And that at the core of their experiences, is this formless, attributeless awareness.   Then the student has to explore the validity of this realization by trying to shake the sense of certainty it brings to them. This happens through repeated logical refutations they must work through until there is no doubts left about their true nature as awareness itself. 
  Nonduality means nothing is apart from awareness - it means every thing is made up of, and is an appearance of awareness to awareness. There is no thing that can exist apart from awareness.