First, there are some external actions you can do to clear away some of the noise of your day. One is to disconnect – turn off the radio as you're driving to work, put your cell phone on “do not disturb mode” at times throughout the day, shut off 24-hour news on the television, and so on. Do this intentionally to create space for silence, both physically and inwardly.
Second, do a little spiritual multitasking: Practice silencing yourself inside even while you are busy and noisy outside. Put down the cell phone and pick up the soul phone. Take a breath. Take another breath. Think about your spirit. What do you need right now? Help? Love? A good word? Sympathy for the speaker? You may be able to achieve only a moment of holy silence at first. Don't despair; with practice, you'll do better.
Third, consider holding silence, as we Quakers say. We hold it – in our souls -- as carefully as you’d hold a baby bird in your hands: gently, softly. That is because, like a baby bird, holy silence can be easily crushed. Holy silence calls for that same sort of holding lightly, of attention from the deepest resources of your being. Pay attention to whether you're grasping desperately for silence or allowing it to be held gently in your soul.