Paul,
To experience nonduality or SR as they call it here, you have to rise above your mind. You can read tons of books and articles but to experience it, takes time......well at least from my experience.
If you still find it hard to understand, I ask you to refer books written by - Nisargdatta, Sri Ramana Maharishi, Mouni Sadhu.......probably any books on Buddhism, Hinduism..etc.
I have found this link which explains in simple words.
Nonduality - A Practical and Experimental Approach
As mentioned before, its the practice of concentration and meditation that bring you closer to experiencing nonduality. Let go of all previous beliefs and let your practice guide you.