JOEL - We not only find the truth in prayer, but we also find it in our studies of the scriptures; the fruits that we see coming from the Church; and in the blessings we receive by our obedience to the doctrines that we receive from the prophets. All of these including prayer and a witness from the Holy Ghost help us to determine the truthfulness of what our prophets tell us. All these are important in making sure our answers are coming from the right spirit.
Here are a few supporting scriptures:

"Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit. A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit. Wherefore by their fruits ye shall know them." (Matt. 7:16-18, 20).

Here is a partial list of the fruits of our religion that helps to validate its truthfulness and devine origin:

1. Happy, healthy, stable families.
2. Expressions of service and love to fellow man.
3. New scripture prophesies and revelations from God.
4. Church organization the same as Jesus established in the primative church.
5. Faith, repentence, baptism, and Holy Ghost.
6. Miracles and gifts of the spirit manifested.
7. Rejection and persecution by the wicked.
8. One of the fastest growing religions in the world. Missionary activity.
9. Millions of members dedicated to living and serving in the Gospel.
10. Millions of dollors worth of humanitarian aid distributed throughout the world.
11. Healing the sick through priesthood administrations.
12. Answers to life's questions. Why are we here? Where are we going? How do we get there? The plan of salvation.
13. A sense of love, devotion, and service to God and community.

What kind of fruits came out of the Branch Davidian group? Mostly a lot of false prophesies and a self-serving leader who led his group to destruction. I don't see that happening to the LDS Church anytime soon.
We are encouraged to study the gospel rather than to blindly follow one person:

"But, behold, I say unto you, that you must study it out in your mind; then you must ask me if it be right," (D&C 9:8)

And as all have not faith, seek ye diligently and teach one another words of wisdom; yea, seek ye out of the best books words of wisdom; seek learning, even by study and also by faith. (D&C 88:118) (See also Moroni 10:3-5)

We also must try to put into practice what we have learned, to see if it is true doctrine.

"If any man will do his will, he shall know of the doctrine, whether it be of God, or whether I speak of myself." (John 7:17)

We will realize the truthfulness of what our prophets tell us after we follow their councel and observe the blessings that come from it.
All of these things are important when trying to determine the difference between a lying spirit and a true spirit.
Of course there are going to be other religions who will say similar things about themselves; there's no absolute perfect test. If there were everyone would be a Mormon. We make our choice and go by faith that what we have chosen is the right way.