It's hard for anyone to do what I call cold turkey evangelism which is walking up to someone and just start talking about Christ. There are people I know who have to true gift of evangelism and can do that then bam that person is saved. You are probably saying well I can't do it that so I guess I shouldn't go evangelizing. Well, does that mean we shouldn't evangelize? No, Jesus told his disciples before He left this world to go into the uttermost parts of the world and preach, teach, and baptizing them in the Holy Ghost. So though some of us are not anointed to preach, teach or evangelize we are still called to do the work.
Here are some ways to share the gospel without feeling like an idiot. When you go out thinking that it's business as usual ask God to send someone that you can share the gospel with. Or when you're talking with a stranger find an opening that allows you to share Christ. I have found that for me this is the best way to minister to someone. I've been at restaurants, starbucks, clothing stores, or even just walking down the street and God as led me to minister to someone. If your looking for a way to talk about God then He will provide a way to make it happen. When you go out always have a mindset that God is going to open an opportunity for me to share His love.
Or this is one of my favorite ways to evangelize it's called indirect evangelism. When I'm with my dad God has shown him something about a person sitting at another table. He'll just starting talking about that certain issue God impressed on his heart and then God starts to move on them. He's had people start getting uncomfortable or some came up and say you were talking about me.
So don't be afraid of peoples faces but when you gain an understanding like Jesus and how he saw the hurting and the lost you won't be fearfully.
Make sure in your life you have a mix of staying in your word, prayer, discernment, and the power of God you can share the gospel of His cross and be bold.