how to know if The Book of Mormon is true

"Now, we will compare the word unto a seed...

"...If ye give place, that a seed my be planted in your heart,

behold, if it be a true seed, or a good seed,

if ye do not cast it out by your unbelief,

that ye will resist the Spirit of the Lord,

behold, it will begin to swell within your breasts;

and when you feel these swelling motions,

ye will begin to say within yourselves -

It must needs be that this is a good seed, or that the word is good,

for it beginneth to enlarge my soul;

yea, it beginneth to enlighten my understanding,

yea, it beginneth to be delicious to me...

- Alma 32:28 

It's as simple as that. To know if the Book of Mormon, or anything else for that matter, is true; all you have to do is give place for it in your heart - read it!
And if it does these things - swells within you, enlarges your soul, enlightens your understanding, and  becomes delicious to you - then you know its true!

"But behold, as the seed swelleth, and sprouteth, and beginneth to grow,

then you must needs say that the seed is good;

for behold it swelleth, and sprouteth, and beginneth to grow.

And now, behold, will not this strengthen your faith?

Yeah, it will strengthen your faith:

for ye will say I know that this is a good seed;

for behold it sprouteth and beginneth to grow...

-Alma 32:30

"But if ye will nourish the word,

yea, nourish the tree as it beginneth to grow,

by your faith with great diligence,

and with patience,

looking forward to the fruit thereof,

it shall take root;

 and behold it shall be a tree

springing up into everlasting life."

-Alma 32:41