Introduction

3rd Paragraph - "...what they must do to gain peace in this life..."
The people of the world all want to be happy.  The Book of Mormon teaches us what we must do to be happy.  If we study and apply the teachings, we will be happy. Mosiah 2:41 - Consider the blessed and happy state of those that keep the commandments of God.


5th Paragraph - "...new and additional witness that Jesus is the Son of God..."
Our purpose on Earth is to be instruments in the hands of God to help others come unto Christ (Alma 29:9).  One effective way to do that is to share the Book of Mormon.  It teaches the laws and ordinances of the Gospel, and if we follow those, we are coming closer to Christ, and we will receive salvation by following that path.


6th Paragraph - "...most correct of any book on earth..." 
Although Joseph Smith makes this statement, which may seem bold, he doesn't degrade other books like the Bible.  I'm sure he would have been quick to say that although plain and precious parts were removed, the Bible was a close second in revealing truth. See Article of Faith #8. He does say that it is the most correct.  Studying and following the teachings within the Book of Mormon will also be the most effective means of helping us against Satan and his forces.


8th Paragraph - "...those who pursue this course and ask in faith will gain a testimony of its truth..."
After explaining the invitation to ask of God, a promise is given that "those who pursue this course and ask in faith will gain a testimony of its truth and divinity by the power of the Holy Ghost."  The key words I think are "pursue" and "faith."  This is another example of working and demonstrating your faith, and then learning to recognize the response from the Holy Ghost.  If we really want an answer, we need to develop our faith through faithful actions.  Then we can receive the truth of all things...line upon line, as we need it and can handle it.