ANSWER: The most important thing to remember is you ultimately cannot change your wife or anyone else for that matter. You can only change yourself. In fact, trying to change others can result in the loss of a friend, a divorce, or even worse. It is God's job, not mine, yours, or anyone else's, to convert your wife, as the Lord stated in John 6:44.
When I was much younger, I was told that if God says something twice he wants to be sure we get the message. Well, Jesus repeated the fact that only the Eternal can bring someone to repentance and conversion when he states just a few verses down in verse 65, "For this reason, I have said to you, no one can come to Me unless it has been given to him from My Father."
In spite of what many religious people believe, the Bible states your wife will NOT go to an ever-burning Hell if she does not accept Jesus before she dies (see our articles entitled "What does the Bible say about Hell" and "Meaning of the Rich Man and Lazarus parable" for more information). God has a plan for every human. He might call your mate to repentance in this life or wait until the second resurrection to do so.
What should you do and NOT do?
Do not flaunt your piety to your mate or to others. Do your bible studies in private and do not push your favorite scriptures onto her. Ask God, if it is His will, to convert your spouse in this life. If your wife has a question, answer it as simply as possible. This will leave the way open for more queries.
Set a simple but Godly example in everything you do. If you have little children, read them a story from an illustrated children's bible at bedtime and teach them to pray. Be patient in traffic, show kindness toward everyone, and be honest in all your dealings. In this last regard, a friend told me this experience from her bus-driver father's life.
A well-known minister was coming to town, and pictures of him were everywhere: on billboards, in newspapers, in store windows.
The minister boarded the bus to the town where he was to preach. As he counted his change, he discovered the driver had given him too much. "Oh, well," he mused. "It's only a quarter. The driver won't miss it." However, his sense of honesty told him it was not his, so he should return it. The mental argument went on and on but, when he arrived at his stop, the minister told the driver he had given him too much change, and returned the money.
"I know," said the driver. "With all the pictures everywhere, it was easy to recognize you. I gave you the extra quarter to see if you really practice what you preach." When he got off the bus, the minister slumped down on a bench and cried, "Oh God. I almost sold you for a quarter."
It is your spouse's decision whether all this helps to change her mind about Jesus and Christianity. However, if it does not, remember the Apostle Paul's admonition in 1Corinthians 7.
If any brother has an unbelieving wife, and she consents to dwell with him, let him not divorce her . . . the unbelieving wife is sanctified in the husband; otherwise, your children would be unclean, but now they are holy (1Corinthians 7:12 - 13).
Finally, do whatever you can to live peaceably with your wife (Romans 12:18) and leave it to our Father in heaven to convert her.