Jesus told His disciples again and again, "Fear not!" Fear, anxiety, worry -- are all about the future when we don't know what will happen. The future is not something we can control, even if we manage to do everything needed in the present. This sense of powerlessness adds to our fears. Even when we think about the promises of God, we are stricken by the memories of things that have gone wrong for us as well as the others in the past, and we wonder if things will go well for us now. The Devil tells us that we are not good enough for God and that we will always be imperfect in whatever we do, and so we can't expect God to keep His promises for us, even if He has kept them for others! Even though we try to think that we have faith in God's promises, our mind tells us that we do have doubts!
One big mistake we make is when we disassociate our faith from our relationship with God. Some people try to work up their faith by positive thinking and confession, repeating Bible verses to themselves, resisting doubts, etc., and think that when they get to a state (hopefully!) where they have no doubts at all, then they can get what they want with their faith. The mistake is that they think it is their faith that brings the miracle, not recognising the fact that in this they are depending on their faith and not on God.
Some others happily receive truths about God, agree with them, and think that now they have faith and that God will make everything work out fine for us. Here the mistake is in assuming that 'faith' in our head will automatically bear fruit.
Yet another mistake is to imagine that when we have faith God will always keep us free from problems or when the problems come He will immediately snatch us out of them. But in reality we all go through many problems and they don't just go away when we pray (Jn.16:33;Ac.14:22).
Faith, at its root, is essentially our confidence in God. It is He who has the power (Ps.62:11) and not our faith or words. It is He who will do great things when we trust Him, and it is not we who will accomplish great things by our faith. When the time of trial comes, if we place our confidence in God as our heavenly Father who loves us, cares for us, knows everything that is happening to us, and who is mighty to do whatever He thinks is best for us, then our anxiety will disappear. Not when we try to think positively, imagining we are holding on to God's promises. We shouldn't be holding on His promises in the place of holding on to Him who has given the promises.
When we hold on to God when we face trouble, we know we are safe like children holding their father's hands. We know He is in control. We can remember how He has led us through the problems even though at that time we had felt it was hopeless (Ps.37:25).
Shadrach, Meshech and Abednego trusted God so much that they left their future in God's hands, and that made them fearless (Da.3:17,18). It is only like this that we can overcome fear.