The answer is very simple to express. But harder to experience. Not because it is hard to achieve, but because our natural, fleshly reactions are always to look at the circumstances around us. We need to look up. Always. Corrie ten Boom said it well: "Look at the world and you'll be distressed; look at yourself and you'll be depressed; look at Jesus and you'll be at rest."
All (and I chuckle as I say the word "all" because it is not as easy as it sounds due to our human nature and the world in which we live that has taught us to do for ourselves) ... but all we need to do is draw closer to God through Jesus. And the reason that is harder than it sounds is that the first step is to deny ourselves. That is the very first step of all: deny yourself. Until we are willing to lay down our rights, our wants, and our perceived needs, surrendering them all to God's will for us, we will never be able to experience His true peace in the midst of the storm. We have to trust that not only is His way best, but that He will always have our best interest at heart-- loving us, caring for us, nourishing us, protecting us and providing for us ... but according to His perfect will, which is rooted in His perfect love for us and His perfect knowledge of all things.
Trust and faith are different words for the same thing. Faith in God is really --very simply-- trusting Him. Trusting Him to be who He says He is and to do what He says He does.
Simple. In theory. But we have to battle our flesh in order to do it. I say "battle" because our flesh does not die easily. It will even submit to religious activity or ritual as long as it is allowed to continue to rule out lives. That is why Jesus said in Matthew 16:24a-- "If anyone wants to come after Me, he must deny himself." Denying oneself means giving up your right to yourself. Giving up your own will and your own ways for God's will and ways. It means surrendering everything to God.
And that is a learned process. How long it takes for any one of us depends on us. It took 40 years for Israel in the wilderness to come to the point where they were so trusting of God and dependent on Him rather than themselves that they were finally ready and able to cross Jordan and enter the promised land. The word Jordan means to go down, to be lowered. God had to break them of their self will and self confidence in order to prepare them to live in total trust (total faith, if you will) in Him ... His direction, His ability, His will. He needs to do the same with us. Then, and only then, are we prepared to undertake the entirety of Matthew 16:24-- "If anyone wants to come after Me, he must deny himself, take up his cross, and follow Me."
Once we are willing to say no to our self and yes to God, we are then able to pick up our cross --which symbolically refers to the fact that we no longer have a life of our own but are under the control of a superior force and on the road to death to self-- and follow Jesus in the way that He leads. And all of this takes complete trust.
Too often we who say we follow Jesus are like the disciples in the boat on the sea of Galilee when the terrible storm hit. They saw the wind, they saw the waves, they saw the water entering the boat, and they were terrified! Jesus, meanwhile, was sleeping peacefully in the boat. His union with the Father was so perfect that nothing could disturb Him. He trusted the Father with His life. Every moment of it. And what were His words to His disciples after He had calmed the storm? "Why are you afraid? Have you still no faith?" In other words, why were you worried? Do you not trust God?
So, keeping this short, we need to trust God that all that is happening in the world is under His eyes and under His power. All that Satan and man are doing that is so evil and destructive has been foreseen by God and allowed for His purposes ... which are always absolutely perfect and will unquestionably result in our eternal good and His eternal glory.
So the answer to getting from shock and fear to peace in the midst of the worsening storm is cultivating trust in God. We can no longer go through life with God in our back pocket, so to speak. He needs to be the very hub of every aspect and every moment of our life. We need to relate to Him truly as to a perfect Father and to Jesus as the one who knows us intimately and cares for us deeply and beyond measure. Work on that relationship, and the peace will come. Focus on God and His promises. If we cling to them, treasure them, trust totally in God, the world will stop frightening or disturbing us.
I pray this helps.