For a long time I went around in circles with this before it "clicked" and the change happened to me.

Everything you need to know is in the phrase "The power of now". What happens is you become absolutely absorbed in this precise instant in time. When that happens the mind seizes up and stops. It stops so completely and absolutely that you would never image such a thing is possible. After that the sense that there is a separate individual "person" vanishes because there is no longer a "person thinking" for the brain to lock onto and identify as a person. When that goes away the experience of oneness opens up... the universe is experiencing itself.

In self enquiry (Ramana Maharshi) you are told to focus on the sense of "I".

"If you hold this feeling of ‘I’ long enough and strongly enough, the false ‘I’ will vanish leaving only the unbroken awareness of the real, immanent ‘I’, consciousness itself." -Ramana Maharshi

Eventually you'll notice that the sense of "I" is only happening in this precise instant in time. The sense of "I" is the sensation of the present moment and everything being perceived.

Watch the mind and notice how all mind wandering self-referential thought comes with a time-stamp. The mind is imagining a person that it calls I/me and that person is being imaged in a time other than precisely now.

Let go of that. It is a phantom and is not you. You are the consciousness that is seeing the mind imagine a person. If you can see it then it isn't you. With that, look at the mind. Look at the body. Look at everything appearing in consciousness. Look at the sense of will and volition. Look at the feeling of "I move the hand".

If you can see it then it isn't you.

What are you? Can you find "you"? Can you see "you"?

In terms of how the change happens, I got lucky as well. One night I was laying in bed with your classic mind of chaos and severe anxiety. That night was particularly bad and I was struggling with an attempt to meditate when suddenly and without any warning the mind just stopped and vanished, and I mean seriously "slam on the breaks" and come to a sudden and absolute screeching halt of absolute nothingness. I literally felt the sensation of a perfect void of nothingness open up and occupy the space where the mind once was. It was a fascinating sensation... even a bit startling in a funny way. All that remained was the universe experiencing itself in precisely "now".

This state remained for about 48 hours and then the mind came back... and then it intermittently turned off and on for about two years before it "stuck" and became persistent.

Now... life goes on. Only now life is lived in stillness.

It's all about the stillness. Be still.