One thing is that God's silence is one of His greatest forms of intimacy. For example, when my family goes on long trips, my wife and I do not spend the entire time in the car talking (that's because she is usually sleeping!). We don't have to. We are comfortable in each others silence, and sometimes, it is more about enjoying the presence of a person than it is about conversing with that person. That is a form of intimacy. It is the same with God.
Silence is also a sign of His trust. He is saying "Just be still and trust." He trust us with His silence to see how we will react. We get into fits when we cannot discern God or understand what He is doing in a particular situation. We get frustrated because we want to have knowledge about situations because we think that if we do, we will somehow have control. Ultimately, it is a pride and control issue. God's silence is a call by Him to relinquish and trust. God's silence is a privilege; one of the greatest forms of intimacy that He can give His children. So many times we see it as a negative thing. We get mad or frustrated with God and begin to question His ways and doubt His character. Rather, we need to rejoice that He has seen fit to bless us with such an intimate gift.
Look at the story of Lazarus in John 11. When Jesus was summoned to come and heal him, what was the response? He waited. He was silent. He didn't go until Lazarus was dead- until it was too late. Or so it seemed. Mary and Martha did not question Jesus' wisdom, but they certainly didn't understand His actions. So what was God after in this situation? Through this situation, not only did Mary and Martha receive their brother back from the dead, they also received a greater revelation of Jesus. It was during this entire episode that Jesus revealed Himself as the resurrection and the life.
God is being silent because He wants to give you something so much better than that which you are craving right now- He wants to give you a greater revelation of Himself, and that only happens in the intimacy of silence.
So what do we do when God is silent or when we are waiting for Him to act? Psalm 37 gives us direction in this area. We must "Trust in the LORD and do good." (vs 3). "Delight yourself in the LORD and He will give you the desires of your heart." (vs 4). "Commit your way to the LORD (the Hebrew literally says "to roll" something onto the LORD- in other words, we must roll all of our anxieties, desires, and frustrations onto Him) . Trust also in Him and He will do it (He will take care of the situation) (vs 5). "Rest in the LORD and wait patiently for Him." (vs 6). To sum it up, we must trust, do good, delight, commit, and rest. It is a call to throw ourselves onto the providence and sovereignty of God. Therefore, when God is silent or when you cannot discern His way or what He is up to, follow the advice of David- trust, do good, delight, commit, and rest. The end result will be a greater revelation of the One who is Himself the Bread of Life.