The Bible does not give specific guidelines concerning sharing one’s faith with the opposite gender/sex. We do have the example of Jesus, who spoke one-on-one to a Samaritan woman about her spiritual need (John 4). And in the book of Acts, Priscilla and Aquila speak to a man named Apollos about the gospel (Acts 18:26); however, they were simply correcting some wrong ideas that Apollos had, not really witnessing to him.
The Bible says that sharing the gospel is a primary responsibility (Acts 1:8). Since there is no biblical instruction to share the gospel only with people of the same gender, we can assume that it is okay for men to share their faith with women, and vice versa. However, there are some practical matters to consider. Discernment in dealing with people one-on-one is always necessary.
A young Christian woman needs to use wisdom in sharing her faith one-on-one with a man. There are men who will pretend to be interested in the gospel when really all they want is to talk to a girl. A feigned interest in spiritual things can mask a more dominant interest in physical things. When a married man shares his faith with a woman, he should take steps to avoid compromising situations or misunderstandings. Many pastors make a point of counseling women only when their wives or another woman can take part in the counseling session. The biblical pattern of witnessing “two by two” can forestall many potential problems (Luke 10:1).
If you have a friend of the opposite sex who is having some spiritual problems or wants to talk about your faith, there is no problem talking to him or her one-on-one, as long as you exercise caution. Pray for wisdom in each situation (James 1:5). In all personal relationships, it is best to pray, approach things case-by-case, and simply use good judgment.