Stopping Mental Noise
Mental noise is usually hard to stop or get rid of because we take it personally.
We can believe the mental noise is our own doing, something that we should be able to control, and so we can feel as if our attention is locked into it in an attempt to fix it.
But notice how impersonal the noise actually is.
Each thought is there before you have even made a judgement on it. Even the judgements are automatic and impersonal, so to say "you judge thoughts" is not really correct.
It's a huge relief to see that the mind and any of its associated sufferings are not as personal as you once thought. To notice that its very nature is impersonal and uncontrolled means that you can regain some space and sense of perspective when the mind chatters or grumbles.
With space comes less resistance, and with less resistance comes peace.
No matter how personal it feels, no matter how much "me" the thoughts seem to be saturated with, see if you can notice that actually, it comes by itself, and it stops by itself.
The Momentum Of "Me"
Mental noise tends to carry a momentum built up by identifying with every thought we have. It has a force of identity, and this force is enhanced when we try to somehow out-think ourselves or stop ourselves from experiencing thoughts.
Once we start to see that the noise is not personal, then it isn't up to us to try to stop it in its tracks anymore. It slows down by itself, when we have less of our sense of self invested in it.
The more you struggle with your mind, the more you feel trapped within it. Give yourself a rest, and release the assumption that the arising of thoughts is your responsibility.