A consciousness shift describes moving from thinking to awareness. It is a sign of awareness (or consciousness) arising within someone. It is part of the awakening process.
Someone goes from being identified with thought or emotion to suddenly knowing themselves as the awareness behind thought and emotion. This is the shift from thinking to awareness.
Consciousness shifts can be very extreme or the can be very slight. Someone may suddenly realise that a certain thought in their mind is just a thought "on repeat", that it is not them, so it can be let go of. Someone else may be experiencing intense fear or some other form of emotional suffering, then suddenly awaken out of their entire false sense of self, becoming the constant still awareness behind all of it. This is enlightenment.
There is no right or wrong way to experience a shift in consciousness, and the more you try to experience it the harder it seems to be.
There is nothing you need to do, just remain as the conscious awareness of your thoughts and emotion. Everything else takes care of itself. It is quite an effortless practice, just observing, quietly watching what your mind or emotions are doing.
Remember that your mental noise or emotional turbulence is nothing to do with you or who you are. Just watch without judgement and see what happens.
Do not label any thought or emotion as good or bad. That means the ego or "voice in the head" has just returned. Just be aware. Accept what arises. This means that the shift in consciousness has already taken place.
The consciousness shift is the most significant thing that can happen to you. Even if it is only minor, it means you are realising what you actually are. The disguise of your body and thought forms are being realised, and you can see that your essence is beyond these things.