Most believers in God have been challenged by those who don't believe in Him by this statement: "You can't prove God exists, therefore your beliefs are built on blind faith." This is meant to put the burden of proof on the believer, who then has to admit that he cannot really prove that there is a God. This implies that it is foolishness to believe in God when you cannot prove His existence.
I think that this type of statement is really nothing more than a smokescreen atheists use in an attempt to free themselves from responsibility to God. I have known a few atheists and have found that, at least with the ones I have known, they are really not unbelievers. I theorize that the issue with my atheist acquaintances is not really that they don't believe in God (as they claim) but rather that they are mad at God. They really do believe in God but are mad at Him because He doesn't meet their expectations. They in turn ignore Him or deny that He even exists as a way of paying Him back for not being a God of their liking.
So what do you do when someone asks you, "Can you prove that God exists?" First, begin by trying to assess the motive behind the question. There are at least two possible motivations for asking this question. The first possible motivation is antagonism. This happens when a skeptic tries to put the burden of proof on the believer. The antagonist is not really seeking answers but is seeking a fight or trying to make the believer feel foolish. The second possible motivation could be a genuine search for answers. The question is asked with a sincere desire to know if God can be known.
Once the motivation is determined, then I would suggest beginning your defense with Scripture. Explain that you believe that God has revealed Himself to man within the pages of Scripture. Your faith is built on the truth of God's word and you are not ashamed to use the Bible as your starting point. Challenge your atheist friend to read the Bible for himself. You can then point out that God has revealed Himself to man in three ways: the Scripture, the creation, and the person of Jesus Christ. It is this person, Jesus, whom you have a personal relationship with. Who can argue with that?
Now you can put the burden of proof back on the atheist. Ask him if he can prove that God doesn't exist. The atheist will have to admit that he cannot definitively prove that there is no God. Therefore, his claim that there is no God is based on blind faith. Now you can follow up with logic. Since neither side can neither prove nor disprove God's existence, which stance seems more logical? A believer can point to all the design in the universe as being more indicative of a Designer than of random, undirected processes. This is only logical. An argument for God can be made from the fact that morality exists. In an atheistic, materialistic worldview, morality shouldn't matter. The existence of God is bolstered by the fact that there is such thing as morality. Why does it bother atheists to see children injured or innocent lives lost in a tsunami or other disaster? It is because they know that those things are not good. But good is a moral term. How do purely materialistic organic lifeforms instinctively know that little children shouldn't die? Why does it even matter unless there is a God?
Don't be intimidated by atheists. Christians have answers.
The fear of the Lord is the beginning of knowledge; fools despise wisdom and discipline. (Proverbs 1:6-8) HCSB