Read up then. I would advise reading the whole Bible all the way through, and taking time to understand it. Unbelievers have a tendency to make fallacious and slanderous claims about the Christian faith based on certain Old Testament laws and stories. Such people fail to understand the lesson to Christians in those stories. The Old Testament has many profitable lessons and morals for us, but Christians who were not born Jewish have no obligation to follow the entire Law. You should read up on what Jews believe about this matter too, they believe that their tradition on what the Gentiles are to follow vs. what Jews are to follow is older than the New Testament itself, which is important - Christians didn't make that up in order to avoid certain commands, Jews were already teaching it at the time.
Study up on logical fallacies. Our faith does not rely on these fallacies, but many immature Christians have used fallacious arguments in presenting the faith. Unbelievers commit them too, when criticizing Christianity and when presenting their own alternatives. If you commit a logical fallacy in a hostile environment on the Internet, you instantly lose all credibility.
http://www.logicalfallacies.info/
Read apologetics books. Case for Christ and Case for Faith by Lee Strobel (former atheist) are good first steps that point you to yet more resources. I Don't Have Enough Faith to Be An Atheist by Drs. Frank Turek and Norm Geisler has some good arguments in it and also cites more resources, though it's almost cocky in its presentation. Mere Christianity by C.S. Lewis (former atheist) is more personal and informal about why he converted - it's also morally challenging for the Christian. But don't just take what you read in these books and fire them off like bullets. Take the time to digest and understand them, making the arguments your own while staying true to the facts.
http://www.reasonablefaith.org/ is Dr. William Lane Craig's website. I enjoy reading his apologetics posts that appear on Facebook. He's one of the people Strobel interviews in his books.
For dealing with Jews specifically, Dr. Michael L. Brown has written a number of books. He was born Jewish, and found Jesus as a young man. 60 Questions Christians Ask About Jewish Beliefs and Practices is a brief introduction to Jewish culture today, the face of Judaism has changed since the time the New Testament was written, there are many traditions that have developed since then. It's important to take that into account and not make assumptions. He also has a five-volume series called Answering Jewish Objections to Jesus which has some good information.
Ultimately, you need to remain calm, respectful, honest, and inquisitive. Remember the instructions in James 1:19-21, it is so important.
