There are a number of techniques for silencing thoughts. Only one of these methods, so far as I know, leads to Self-realization. It has been described in a variety of ways by different people. Here is my attempt to explain how to do it.
This method is based on a certain state of mind that you can get into voluntarily. Thoughts cannot occur while you're in this state. The longer you stay in this state, the less effort is needed to maintain it, and the weaker the impulses become that tend to generate thought.
I'll call this mental state "the aware state." Other people have called it I AM, self-remembering, awareness watching awareness, abiding as yourself, and knowing that you are. Although these names sound different they all refer to the same thing.
To learn this method from this article, two steps are required:
1. You have to figure out what I mean by "aware state" and experience that state for yourself and recognize it.
2. After you know what the aware state feels like, you have to learn to make it happen deliberately.
Step one: Recognize the aware state
I suspect that nearly everybody experiences the aware state occasionally without noticing it. Contrary to the impression given by many books, there's nothing arcane or remote or advanced or difficult about it. It's a normal, ordinary state of mind.
(I'm using the word "mind" in its ordinary English sense of "consciousness." Most spiritual books use it in a more restricted sense having to do only with sensation and thought. They do this because the word for "mind" in Indian languages has that restricted meaning. This is one of the reasons why spiritual books in English are so confusing.)
The most difficult thing about step one is figuring out from somebody else's description what the aware state is exactly. It's very hard to describe a state of mind, and most of the descriptions in books aren't very good.
The way I'll handle this problem is by describing a situation in which the aware state occurs. It's easier to describe a situation than a state of mind. If you put yourself in this situation, the aware state will occur, and then (I hope!) you'll know for sure what I'm talking about.
I'm going to assume that you've tried to meditate at least once, because that's when this situation occurs. If you've never tried to meditate, you'll need to stop reading now and meditate for twenty or thirty minutes before you go on. You can meditate in any way you like as long as it involves maintaining your attention in some chosen way. For example, you could try to stay aware of your thoughts. Or you could try to fix your thoughts on a particular object or idea. Or you could try not to have any thoughts at all. Whatever you choose, try to maintain your attention for twenty or thirty minutes. If you lose your concentration during this time, that's okay (in fact, that's perfect, as you'll see in a moment), but as soon as you can, start concentrating again and continue until the time is up.
Now, here's my description of the aware state.
During meditation everybody has the experience of suddenly realizing that for the previous five or ten minutes they hadn't been meditating at all. They got lost in daydreams without realizing it. Suddenly they snap back to their senses and realize, "Oops! I lost my concentration and got lost in daydreams for several minutes without noticing it. I only just noticed and remembered this instant that I was supposed to be meditating."
If the last paragraph isn't familiar to you, try meditating some more until you notice this experience happening to you. The rest of this article won't make any sense unless you recognize the experience I just described.
What does this experience have to do with the aware state? Well, at the instant that you snap back to your senses, you are momentarily in the aware state.. An instant later you will probably begin to berate yourself for abandoning your meditation, causing you to slip back into the ordinary lost-in-thoughts state, but at the very moment in which you come back to yourself, you are in the aware state. (To be precise, you are closer to the aware state at that moment. It's really a matter of degree.)
Keep putting yourself in situations where this experience happens, and each time, try to notice the heightening of awareness that occurs at that moment.
(Incidentally, if you've ever been puzzled by the traditional instruction to look at the space between two thoughts, this is what it's refering to. At the moment I'm describing, your daydreaming just ended and your next thought hasn't yet carried you away.)
As you observe these moments more carefully, you'll begin to see that thinking and awareness are polar opposites. The more you have of one, the less you have of the other. At one end of the continuum, you are lost in thought. At the other end, you are aware.