For me, it happened one day while a friend (also a member) and I were walking through our neighborhood. My old church was in my neighborhood and first, my old pastor drove by in his truck, waving as he did. I waved politely back. Then, another member of that church drove up and stopped, probably on her way to the church. When I told her I was attending the Church of Jesus Christ of Latter-Day Saints, she went into an enormous tirade that left me speechless, angry, and frustrated. I had the words, but I didn't know how to get them out. Instead I sputtered like a fool.
So... don't be like me, but rather, listen to the spirit before you start talking..
My Missionary friends explained it to me like this:
Christ's church is like a stack of Jenga blocks all stacked up together. Over the years after the Great Apostasy, many new churches were formed and people pulled pieces of the Jenga blocks out here and there (ordinances and authority), thinking that they didn't need them and that they were unnecessary. Pretty soon, the Church (Jenga stack) crumbled, and people realized what they had done, and scrambled to piece back the stack (Christ's church). Of course, with all of the new churches, that authority was LONG gone, and even though they tried to bring back important things like Baptism, it wasn't under the authority that God placed under the Earth in Christ's church.
Incomes Joseph Smith. We all know the story and I know that I am grateful that Christ's church has been restored! I'm sure that you have had many other questions, but I will let you go for now with these thoughts:
1. The Missionaries are a great source for specific questions you or your friends have about the Church.
2. Let the Holy Spirit guide your thoughts and speech.
3. Pray about specific questions you need answers to.
I know that as you grow in your knowledge about the Gospel it will get easier for you to explain things to others! :)