We might think of "silent prayer" as communicating with God not by speaking words aloud but by saying them in our minds. But prayer does not always require words. In fact, Jesus cautioned that using "many words" in prayer could become like babbling (see Matthew 6:7).
Being still, without using words, can help us reflect on the majesty, power, beauty, love, and other characteristics of God. We need to be clear, though, that this is different from meditation that views silence as a way to empty the mind of thoughts and to connect with one's "inner self." The command to "be still" in Psalm 46 has nothing to do with that—and is actually the opposite.
Notice that the words "be still" in verse 10 are immediately followed by the instruction to know God. Prayer helps us grow in our knowledge of God, and knowing the heart of God is what enables us to be still in his presence. As Psalm 46 indicates, God is both powerful and kind. Our troubled hearts are quieted when we find our refuge in him.
Some Bible versions include the Hebrew word Selah after verses 3, 7, and 11 in Psalm 46, and that may help us understand this point. Scholars aren't sure what Selah means, but it seems to signal a pause and perhaps a time of reflection.
Practice being silent in God's presence. Quiet reflection intensifies prayer as the mind is filled with thoughts of God.