Through honest study and humble prayer, we can each know for ourselves that the Book of Mormon really is the word of God.
Of course it's one thing to read the Book of Mormon and another to believe deep in our hearts that what it says is true. This sincere belief, or testimony, in the truth of the Book of Mormon comes when God sends His Spirit to confirm the truth of what we read. We can feel this confirmation when we study the Book of Mormon with diligence and faith, as we are promised in the following scripture:
"And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost. " (Moroni 10:4)
God's method is simple: we read the Book of Mormon; we pray and ask Him to tell us that what we've read is true and He answers us through feelings of peace and assurance given by the Holy Ghost. First of all, we have to study the Book of Mormon diligently, applying its principles to our own lives and doing our best to understand the lessons that God wants us to learn. Second, we have to pray "with a sincere heart, with real intent, having faith in Christ." We need to hope and believe that God will answer us, and we may have to pray more than once. Last, we need to be willing to accept the answer when it comes, however it may come. Believing that the Book of Mormon really contains the word of God means that we will be willing to live up to the standards of faith and obedience He describes in it. God has promised that He will bless us with much more than it takes to live up to His high standards.