JOEL - There is no "official" word or doctrine from the church that addresses the existance of the dinosaurs. The only thing that comes close to it is a 1909 statement from the First Presidency on evolution. The fossil records of these creatures certainly affirms their existance at some point of time in earth's history. One of the problems we have in explaining the existance of pre-historic animals is the fact that they suppposedly lived and died millions of years before death was introduced into the world as a result of Adam's Fall. There have been many ideas and theories proposed to explain this dilema.
One theory suggests that the earth was created out of the remains of other planets where these creatures once lived. However, geologic evidence collected so far including; a cooling from a molten state, continental drifts, and stratification of fossils and coal fields, contradicts this idea.
Another from B.H. Roberts, suggested that all life(dinosaurs) prior to Adam was destroyed from the earth, and that Adam and other living things were then transported from another world. Once again, however, the geologic record does not support this.
Some believe that God used evolution to create all things.
Others believe that dinosaurs were created on days five and six with all the other animals and lived at peace in Eden. There was no death among them until after the Fall of Adam because all creatures were created to eat fruits and vegetables. Most of the dinosaurs were then destroyed during and shortly after the flood of Noah. Some people even believe that the "behemoth" talked about by Job in the Old Testament is a description of a dinosaur(Job 40:15-19). However, if all animals were created to eat only fruits and vegetables, how would one explain things such as snakes that have venom, sharks with their sharp teeth and sonar, the tongues of frogs and cameleons, the tentacles of the jelly fish, or a spider's web or the quick arms of a praying mantis, or the meat-eating Venus fly trap?
Another theory suggests that before the Fall of Adam dinosaurs and other living creatures had no spirits and therefore suffered only a type of biological or chemical death. The type of death described in scripture, separation of body from spirit, began after the Fall, with the first soul made of both body and spirit, who was Adam.
As to where the dinosaurs went, there are also a number of theories. Many believe that some catastrophic event, such as the after effects of a meteor hitting the earth killed most of the dinosaurs off many millions of years ago. Others believe that a sudden change in climate across the earth brought them down.
A good answer to this question can be found in a September 1987 Ensign article("I Have a Question") by Morris S. Petersen, professor of geology, Brigham Young University.
He observes that;

"The sequence of the creation of life on earth as recorded in Genesis--first plants (Gen. 1:11-12), then animals (Gen. 1:20-23)--is duplicated in the fossil record: plant fossils precede the appearance of animal fossils. This agreement shouldn't be surprising because the God who created this earth is the same God who inspired the prophets. A conflict arises only when we assume that God has revealed all he is going to reveal on the subject or forget that scientific theories change as new discoveries are made."

Professor Peterson reminds us that, the main purpose of the scriptures is to "reveal why (not necessarily how) the earth was created, and what laws and principles a person must follow to obtain eternal life. The goal of science, on the other hand, is to learn how (not why) the world was made and to understand the laws and principles governing the physical world."
He concludes by saying;
"The relationship between scripture and what is currently understood in science is ever changing. Science continually learns more about the history of life on earth, and we have every reason to believe that much more will be learned as research continues. The struggle to correlate a passage in scripture with a specific portion of scientific research has been a challenge for centuries. But experience has shown that what a person understands today will be modified by tomorrow's discoveries. Patience and humility will eventually resolve all questions--if not in this life, then in the next."

Boyd K. Packer at a BYU Book of Mormon symposium in 1988, declared, "It is my conviction that to the degree the theory of evolution asserts that man is the product of an evolutionary process, the offspring of animals -- it is false! ... And, I am sorry to say, the so-called theistic evolution, the theory that God used an evolutionary process to prepare a physical body for the spirit of man, is equally false. ... How old is the earth? I do not know! But I do know that matter is eternal. How long a time has man been upon the earth? I do not know! But I do know that man did not evolve from animals. ... When confronted by evidence in the rocks below, rely on the witness of the heavens above."

The physical evidence that dinosaurs existed is real and we cannot deny or ignore it. And I don't think God would have just caused fossils to appear in the ground to test our faith.
The best thing to do is not worry about it and know that eventually we will understand how everything was done and why. Someone once said, "God doesn't break the laws of science, he just knows them better than us".
Scientific discovery and religion will eventually find agreement on what is true since the souce of all truth is from God.