There's nothing better than quoting William Lane Craig's thoughts on this issue. William Lane Craig is an American analytic philosopher and Christian theologian, Christian apologist (One of the Greatest), and author. He is a Professor of Philosophy, at Houston Baptist University and Research Professor of Philosophy at Talbot School of Theology.
First I think it's important to realize that doubt is never simply an intellectual problem. Doubt is also I think a spiritual problem. We are involved in a spiritual warfare with an enemy of our souls who hates us intensely and wants to destroy us, and if he can render us ineffective in God's service through nagging doubts and so forth, he will do so. So when we have these doubts we mustn't just treat them as intellectual matters.
We need to treat these as a matter of spiritual concern as well, and therefore redouble our efforts to be sure that we are involved in meaningful corporate worship with other Christians, prayer, Bible reading, and meditation, the typical spiritual disciplines. We mustn't give those up thinking that they're not valuable anymore. And when you walk away and abandon those things you just set yourself up I think for being victimized.
Reason is a tool that God has given us to help better understand and defend our faith, but I think the way in which we fundamentally know that our faith is true is through the inner witness of the Holy Spirit. My faith in Christ is not based upon arguments and evidence, although I have arguments and evidence. It is based upon the inner testimony of the Holy Spirit, God's spirit who lives within me and who, when I cry "Abba Father," bears witness with my spirit that I am a child of God. And so that emphasizes again the importance of cultivating your walk with God, making sure you're filled with the Holy Spirit day by day, that there isn't unconfessed sin in your life, because when you're carnal, that's when these doubts will seem the worst.
If the church loses the intellectual battle in one generation, then evangelism will become immeasurably more difficult in the next. The war is not yet lost, and it is one which we must not lose: souls of men and women hang in the balance.
The chief purpose of life is not happiness, but knowledge of God. People tend naturally to assume that if God exists, then His purpose for human life is happiness in this life. God’s role is to provide a comfortable environment for His human pets. But on the Christian view, this is false. We are not God’s pets, and the goal of human life is not happiness per se, but the knowledge of God—which in the end will bring true and everlasting human fulfilment. Many evils occur in life which may be utterly pointless with respect to the goal of producing human happiness; but they may not be pointless with respect to producing a deeper knowledge of God.
The more I learn, the more desperately ignorant I feel. Further study only serves to open up to one's consciousness all the endless vistas of knowledge, even in one's own field, about which one knows absolutely nothing.
To take a nagging doubt, to pursue it intellectually into the ground until you have come to a satisfactory answer to it, and that will bring a sense of freedom and victory and intellectual satisfaction that the average Christian never experiences because he's never done this. So go after those doubts and pursue them and find answers to them.