Fear and faith are opposing forces. Fear is actually faith in reverse. Fear is believing something or someone other than God. Fear makes us subject to Satan and his death just as faith makes us recipients of all that God has to offer. This is the reason Jesus told Jairus, "Fear not." Jairus' fear would have sealed his daughter's death.
Instead of trying to build huge amounts of faith to overcome our fears and unbelief, a simpler way is to remove our fears by cutting off their source. Our simple "child-like" faith that remains will do the job. It doesn't take big faith, just pure faith.
Where does fear come from? 2 Timothy 1:7 says, "For God hath not given us the spirit of fear; but of power and of love, and of a sound mind." It doesn't come from God. The way that fear is able to come upon us is that we take our attention off of Jesus and put it on our situation.
Fear or doubt cannot "just overcome" us. We have to let it in. In the same way that faith comes by hearing the Word of God, fear comes by hearing or seeing something contrary to God's Word. We would not be tempted with fear or doubt if we didn't consider things that Satan uses to minister that fear and doubt.
Satan tries to distract us with thinking about our problems. No problem is too big for God. We should cast our concern about the problem over on God and just keep our eyes on Jesus, the Word.