Some people are afraid of giving a witness because they may think of giving away big dark secrets. This is not what witnessing is about. You only need to give instances that illustrate how you came closer to Jesus. It does make you vulnerable in one sense. People get to know you. They see you as a person. That is good. You simply want to share with them a positive experience of faith. So it is somewhat personal, but not like something that only your best friend or family members would know. There is an appropriateness in witnessing.
Pay attention to who you are speaking with. Your approach should be based on their concerns. That means that listening is a very important skill. Does the person come from a Christian perspective? If so, were they Catholic at any point? Were or are they Protestant and what denomination? Was their experience positive, indifferent or negative? Do they consider themselves “Atheist”? Some people are not Catholic because of what they think the Church teaches. Be open to saying you do not have all the answers and help them look for the answers. Some people may start with a logical reasoning, but in the midst of the conversation you may discover a more human need. Some people need healing from a bad experience.
Do they sense that you care? Can they trust you if they needed to get something out? Can you find somebody who is willing to help if you feel uncomfortable with that? Sometimes it might be a matter of asking them if they wanted to talk to Father So and So. If they are Christian, maybe you could pray with them. Don’t wait till after the conversation. Pray with them if there is a need. They might need to hear your prayers. If they need hope, you can simply ask God for the gift of hope in this time and end with the Glory Be. If they need God’s will, ask the Holy Spirit for wisdom, understanding and counsel, and end with the Our Father with a focus on “Thy will be done”. Ask the Holy Spirit to guide your words and actions. Among Protestants, the Our Father and Glory Be are safe prayers that they can appreciate.
Atheists can be militantly anti-Catholic and others can be warm to the idea of becoming Catholic. Some do not become Catholic because they think the church members do not want them. Some people call themselves “Atheists” because they do not believe in a God that is mean or enjoys killing. They think Christians enjoy a God that does these things. You can let them know that you do not believe in that kind of God either. It might be an opportunity to share your experience of God’s love.
If the person is not open to Jesus or the Church, then there is nothing you can do. Some people just want to argue. Do not waste your time with them, they are not ready yet. If you try to push it, it will only disrupt the peace of Jesus in your heart. Pray for them and leave it to Jesus.
You are not there to make a full conversion of the person in that setting. You are just an instrument of God to help them come closer to Jesus. Our hope is that they experience God’s mercy and take one more step closer to Jesus. The most important thing is that God’s will is done. We cannot make anything happen without the gift of the Holy Spirit. Trust that He is always there.