A visitor writes,
"How do you explain God's existence to those who refuse to believe in him?"
That's a tough one. Sometimes there is absolutely nothing you can do. Sometimes people don't want to be convinced and aren't open to even considering God until something bad happens in their life. You can bear witness even to such people though. As Peter says: But sanctify the Lord God in your hearts: and be ready always to give an answer to every man that asketh you a reason of the hope that is in you with meekness and fear - 1 Peter 3:15
You never know what effect you have on people. Even though they don't appear to be interested, something may happen in their life one day to make them more receptive to God's word and they might remember some of the things you once said to them. This sort of thing happens more frequently than you might think.
What are the main evidences for the truth of the Bible that are effective in witnessing to others?
Here is a link to a book in the library section of the website by David M. Pearce that deals with the issues around evolution and creation:
Evidence for Design (Click on the title)
Another good reference on the topic of the existence of God is "Gods Truth" by Dr. Alan Hayward. http://www.thechristadelphians.org/htm/books/Gods_Truth/Gods_Truth_mainframe.htm
I hope this has been helpful.