One does not keep their mind off thoughts; one keeps their mind on one singular thought as Awareness. A single thought is another word for awareness. You are aware but not thinking about what you are aware of. This is Awareness.
Ceasing the thinking mind is like listening to someone talk in principle. When you listen to one person talk, you stop listening to others. Particularly if it something you are really interested in attending Consciously. Your conscious mind can and should only be employed properly on one thing at a time. You want your consciousness, your presence to be one-pointed and concentrated, not filtered like a kaleidoscope going this way and that. You know what it's like trying to listen to two people at once. It is frustrating and almost impossible, isn't it? You do not want to divide your house like this. It will unsettle you emotionally and you need your subconscious to be as a peace as one is consciously.
Jesus (True Self) knew their thoughts (mind), and said unto them, every kingdom divided against itself is brought to desolation; and every city or house divided against itself shall not stand.” ~Matthew, 12:25
A house divides itself when it divides itself in thought. When the being mind becomes a thinking mind it is because one thought has become legion - more than two. One thought wants this, and one thought wants that. Both eliciting waring emotions. This is one's temple divided against itself. You don't want this. This renders the egoic state that is full of illusion.
Your natural state of being is mediation, therefore in a sense you could say that we are practicing being our ourselves by ceasing being what we are not. We simply take away what is inhibiting the full expression of our being multi-dimensionally and that would be 'incessant thinking'.
This is how the true Self is revealed. It is revealed when the veil covering its fall away. That veil is the thinking mind that renders a false sense of personal being while ignorant of one's impersonal and eternal state.
This is meditation. Holding the mind that is the vessel of our true Self as Consciousness - the Inner I - singular in and of the awareness that constitutes the subconscious and present moment. Awareness is the subconscious that is ever in the now and which merges with one's true Awareness of being which Soul being Spirit (Consciousness).
We practice keeping the mind focused on one thing such as the breath or a flame as practice for keeping the mind singular in and as Awareness. This Awareness is the body of your singular thought that is in the world as the present moment.
It is much easier to train the mind to be still with an object than to do so without an object which of course Awareness is. So, practice this first if it helps.
Being conscious of being awareness is a non-objective experience as our true Self is not an object but an activity of being that is formless. We practice keeping the mind single so that it can sit within the present moment both consciously and subconsciously, resting in peace as a pure channel for the Spiritual Realms to flow through and into the world.
Remember the mind is like a cup. "The usefulness of a cup is in its emptiness" - Bruce Lee
Become conscious of being Awareness. This is the highest meditation.
~ Tracy Pierce