How do you witness to an atheist?

There are many Christians that accuse atheists of doing nothing but mocking Christians and calling them names (and rightfully so, because it does happen a lot).  However when trying to witness to atheists most Christians like going to Psalm 14:1 and Psalm 53:1 stating that only fools don’t believe in God.  While this is true, this is doing the exact same thing we accuse them of doing.  When witnessing to anyone it is important not to insult them or their intelligence.  Stick to the facts, be ready to answer their questions, if you don’t know something then admit it, and give them the gospel in love (1 Corinthians 13:2).