Have you ever been asked to do something that caused you great anxiety and fear? If so, you know the feeling of angst and wonder how you'll get through that which causes such nervous tension. And yet, in this chapter, Paul writes about sending Timothy to Athens to spread the Gospel of Christ as a way to strengthen and encourage others in their faith, and he does it even knowing he and others who were sent would be persecuted. Let's not forget that there is also the fear that Satan would try to tempt him, others and even ourselves from doing that which our Father desires.
For me, it would seem much easier to agree to talk to people who already have faith than to try to talk to others who know little or none of what faith is about because faith is simply believing in something that we don't actually concretely "see".
As other's see and hear about our deep and committed faith, despite all the trials and tribulations life throws at us, it's that sense of calm that draws people in and wondering how they can have that too. So like Paul and Timothy and all the other Apostles, God's desire is for us to share the love of God and that often means, that sharing with non-believers brings more angst and anxiety than we are comfortable with. So how does one work through being comfortable spreading the Gospel of Christ when this is not your spiritual gift?
I've always found that praying for the person that you are sharing with, is the best way to start and then sharing your faith in hopes that their hearts are open to receive your words. Over time, you can share parts of the Bible and the stories told and even provide different resources where they can learn more about Jesus or even invite them to join you at church or a bible study or a presentation. In time, they may make a conscience choice as to whether they want faith or not and if they do, they can simply ask God to give them the faith they need to believe.