The best vocalization I have found of practical non-dual instructions come from Tibetan Buddhist meditation master Padmasambhava:

...the observer and the process of observing are not two different things.

When you look and observe, seeking the one who is looking and observing,

since you search for this observer and do not find him, At that time your view is exhausted and overthrown.

[...]

The process of meditation and the one who meditates are not two different things.

When you look for the meditator who is meditating or not meditating,

since you have searched for this meditator and have not found him anywhere,

at that time your meditation is exhausted and overthrown.

Thus, even though it is the end of your meditation, this is the beginning with respect to yourself.

The meditation and the meditator are not found to exist anywhere.

Without its falling under the power of delusion, drowsiness, or agitation,

your immediate un-fabricated awareness becomes lucidly clear;

and this unmodified state of even contemplation is concentration.

Therefore remaining in a calm state or not remaining in it are not two different things.

I'm totally not entitled to say the following, since I'm neither a Vajrayana practitioner, nor a the student of a Dzogchen teacher (the above text is talking about Dzogchen), BUT I will offer a few of my little amateur experiences that may correspond vaguely to the text:

What's being 'exhausted and overthrown' in that text? I dunno, but I have a hunch: we often have this intuition, from the first-person-perspective, that our experience is orcanized in a very specific way. There's a 'you' on one side of something that feels like a wall (maybe it's the bone of your skull, if you like that brain-centric view), and then there's the rest of things which 'are in the process of being observed out there,' seen by the you that is on the other side of that wall or in the skull.

But, when we really start look into first-person experience, and how it's really organized, then our intuition doesn't seem to withstand scrutiny: once we try to find a single sign of whatever was behind the wall, whatsoever, it's not there (not even a peripheral sign that there's something behind the wall, like the wake of a boat is noticed behind a moving boat). How's that related? That's just 'no self,' like a hole in our heads.

But if we continue the process of investigation, we see that the previous wall itself still does appear, (there is a distinct point where vision starts and stops, you don't have eyes on the back of your head, or five ears, there are clear points where inputs seem to start and stop) BUT that line that marks where your senses are, the line and the objects of consciousness are both appearances, not completely distinct parts of the first-person experience like the inutive-stance thought before.

So that's pretty much it. It's the removal of that intuitive view of the 'wall' of perception which can takes us from duality to non-duality. There are other ways and versions and instructions, but the most basic, common feature is that the 'wall' between the experiencer and what is experienced, that is collapsed in one way or another (by investigation, reflection, jhana, altered consciousness, whatever).

Now, some people can make an extra step and say, 'That wall and the objects are not different, AND therefore I think that they are both being held IN THIS thing (call it the Self that contains the conventional self, whatever seems to hold all objects of consciousness);' that's where we get non-dual monism (a 'oneness-view' that results from this kind of investigation, I think Vedanta is sorta like that).

I find that intuitively appealing, but sometimes I find it unnecessary, depending on who I'm talking to (i.e., case by case). Some people who took that leap have built a whole structure of god-beliefs on top, and then became very emotionally invested in this assumption that awareness is some sort of God, and when I point out that you can have a very similar experience without assuming that awareness is God, then they get so very upset. I'm just asking questions, because I also want to know what's necessary to have what experiences. But other Vedanta-types don't have that problem at all. And I've also been at those points where I over-invested in some things (like the 'no-self' hole in the head view), and it struck a nerve once someone criticized whatever foundation I put all my weight on top of.

All good, I have met many monists who don't have this problem whatsoever, and met many Buddhists who are waaaaay over-invested in their views about non-dualism. It's really a case-by-case thing, when it comes to practitioners, in my experience.