There are three questions that I offer those people who ask about why I am a believer.  If they are being argumentative, I usually don't engage.  What's the point.  They just want to argue.  But if they are actually interested, I give them the path that everyone has to take sometime in their life to make decisions about God.   Three questions:

1.  Do you believe that there is some power out there beyond human existence?  Call it a creator, God, Supreme Authority, etc.  If they answer no, the conversation is done.  But if they say yes, then I ask....

2.  Do you believe that "God power" is good or evil?   Of course, you have to assume that the person can tell the difference between good and evil.  There seems to be a universal agreement as to what is good and what is evil.  If they say evil, you can agree that there is an evil power in the world where humans are concerned, but for the rest of creation, trees, the world, space, moon, stars, etc.  The creator of all of that--most would say is good.

3.  So...If there is a higher power...and if he is good, then:  How could a good God leave us humans on earth with no answers as how to reach Him.  Communicate.  Know what He expects of us.  Notice my mathematical interjection, If-then.  

Sometimes at that point you get to explain how you got there.  1.yes, 2. yes, 3. yes, point of discovery in your own life.  I like to tell about my journey to figure out if Jesus was God--since Jesus is the only voice in history that spoke for God, and was good, and exhibited authority over a bunch of historic laws that were a burden to people. 

I love this one: you can help a cow out of a ditch on the Sabbath, but not a man.  That would be work.  I guess you just let him lie there with a broken leg or whatever until the next day.

The apostle Thomas was the answer to that question for me.  Give me a good doubter who asks the right questions. Thomas questioned, and ended up saying, "My Lord and my God."