I cannot say how another might silence the mind - I can only share what I have discovered - for years I attempted to "meditate" but always with instructions that involved the mind as manipulator (breathing, sitting in a certain way, thinking about what was being applied etc.) It was only when I received very specific instructions in a simple technique that I knew I had just for the first time experienced meditation. The technique involved no thought, no ideation, no conceptualiztion - just the installation of an app, as it were, into the mind - the replacement of all the buzzings by simply listening to two syllables which had no relationship to "the world" or to "meaning" and that did it - one had only to listen to these two syllables repeating themselves within in order to have all else disappear from the mind. Only two criteria were applied: is it easy and is it pleasant? This is the function of the mantra - to erase the buzzings, to silence the mind - to allow the deeper mind to emerge. There are many ways to meditation. I am attuned to sound, so mantra meditation was natural to me. Now I listen to the entire Agni section of the sAmaveda as my daily mantra - this took some doing, a lot of "work" as it were, but it is the single most valuable task I have ever performed in my life. It's benefits exceed any manipulative, conceptualizing, mentalizing techniques I have tried over the years.
No exertion. No tension. No thought. No nothing. The mind becomes still. It is a revelatory process.
I don't presume to instruct or impart, I simply know what works for me. That is all. The biggest hurdle, roadblock, whatever, is our penchant for the complex, and our refusal to believe that something so simple could possibly be of any use whatever.