You simply have to surrender to the present moment. Be alert. Watch something in a state of alertness. Always, continuously, bring that into everyday life, not spirituality here and getting on with your life there.
If the price of peace were a lowering of your consciousness, and the price of stillness a lack of vitality and alertness, then they would not be worth having.
When you take your attention into the present moment, a certain alertness arises. You become more conscious of what's around you, but also, strangely, a sense of presence that is both within and without.
To be aware of little, quiet things, you need to be quiet inside. A high degree of alertness is required. Be still. Look. Listen. Be present.
If uncertainty is unacceptable to you, it turns into fear. If it is perfectly acceptable, it turns into increased aliveness, alertness, and creativity.
When you become aware of silence, immediately there is that state of inner still alertness. You are present. You have stepped out of thousands of years of collective human conditioning.