When it comes to the story of Adam and Eve, the majority of the Christian world has one interpretation of the story. That Adam and Eve (especially Eve) messed up and we are all pretty much damned because of it. While Latter-Day Saints believe in the same story, we have a different interpretation that isn't quite so doom and gloom.
Though we believe that they did in fact disobey God's law, we also believe that it was not a "sin" but rather it was a "transgression" and though we feel the effects of it just as a child growing up feels the effects of the decisions of their parents, we do not believe that it is something we need to be forgiven of. Hence we do not practice infant baptism for "original sin."
The second more positive interpretation of the Adam and Eve story has to do more with Agency. Agency is the name given to our ability to choose right and wrong. We use our agency to be righteous or wicked. One of my most favorite chapters of scripture is 2 Nephi 2, where it talks about the importances of this agency:
11 For it must needs be, that there is an opposition in all things. If not so, my first-born in the wilderness, righteousness could not be brought to pass, neither wickedness, neither holiness nor misery, neither good nor bad. Wherefore, all things must needs be a compound in one; wherefore, if it should be one body it must needs remain as dead, having no life neither death, nor corruption nor incorruption, happiness nor misery, neither sense nor insensibility.
It later explains in that same chapter how this plays into Adam and Eve's story:
22 And now, behold, if Adam had not transgressed he would not have fallen, but he would have remained in the garden of Eden. And all things which were created must have remained in the same state in which they were after they were created; and they must have remained forever, and had no end.
23 And they would have had no children; wherefore they would have remained in a state of innocence, having no joy, for they knew no misery; doing no good, for they knew no sin.
24 But behold, all things have been done in the wisdom of him who knoweth all things.
25 Adam fell that men might be; and men are, that they might have joy.
Though Adam and Eve disobeyed God's law to them, they only had a partial understanding of what it meant to sin, as they did not have a knowledge of good and of evil until after they had partaken of the fruit. Their actions had consequences (the introduction of both physical and spiritual death into the world) but it was not something that condemned them. They committed the act in their state of innocence and hence were covered by the Atonement just as the wrongs of little children before they know better are covered by the Atonement.
As their children, we honor Adam and Eve for making the decision of beginning the human family and of beginning our Earthy experience. Maybe it was a combination of being tricked by Satan and choosing for themselves this necessary path to jump start the world, but in the end I am grateful for them and what happened in the garden of eden.
When LDS children are taught about Adam, they learn a song about the Old Testament Prophets called "Follow the Prophet". The first verse goes:
Adam was a prophet,
First one that we know.
In a place called Eden,
He helped things to grow.
Adam served the Lord
by following his ways.
We are his descendants
in the Latter-Days.
Though trying to understand the intricacies of The Fall is something that I have been working on for years, I'm comforted by these scriptures insisting that it was not only a fall downward from where we could live with God, but also a fall forwards towards us returning to him again someday.