The Bible tells of so many experiences where fear is conquered. Putting our trust in God, Spirit, gives us confidence that all will be well. Doubt in God's care brings on fear. A little child has certain trust and complete reliance that his parent will keep him safe. We can begin to understand that our connection to God is a lot like that parent/child relationship. Mary Baker Eddy, the discoverer of Christian Science, puts it this way in Science and Health with Key to the Scriptures: "Father-Mother is the name for Deity, which indicates His tender relationship to His spiritual creation." (Page 331)
Instead of thinking that God is out there somewhere, looking in on us once in a while, we can know that God is right with us all the time – as close as our thought! When we have the inspiration and conviction that everything God made is good and that God makes everything that exists, we are freed from fear. Fear can only come in with the opposite conviction that bad exists somewhere to harm us.
Paul says, in I Thessalonians 5: 21: "Prove all things; hold fast that which is good." In my experience I've seen when I completely stop fearing some problem it goes away. I had a little growth on my forehead for a long time. One year I had an insight, a strong conviction that God never made it. From that point, all concern and fear of it was wiped out of my thought. Not long after that it got worse, but that didn't alter my confidence that God never made it. Soon after, it just dropped away and has never returned.
"Hold thought steadfastly to the enduring, the good, and the true, and you will bring these into your experience proportionably to their occupancy of your thoughts." (Science and Health with Key to the Scriptures, page 260.)