I like to think of it this way (this is not gospel doctrine - ok).

If we look at the pattern of development in our day: babies are born to parents. They are not developed enough to make righteous choices and therefore, are protected until they develop to the point where they can make righteous choices.

We could possibly apply that to evolution: we (humans), evolved naturally. As we became the various forms of pre-human, all the while we were being protected and instructed: taught how to survive, grow food, make structures, etc. I think there's plenty of archeological evidence to suggest that there have been civilizations for well beyond the time period of the bible.

Like adolescent children, it's possible that these pre-humans were not evolved enough to be able to make righteous decisions on their own. Could they have kids? Build cities? make war? Yeah, sure. A 7 year old with a full grown body could do those things - but mentally, we're taught, that they are not developed enough for baptism.

So, we pre-humans evolve to the point where one man is born (similar to the first human born with blue eyes, or something), Adam, who is finally evolved to completion. From him, God takes his DNA (the figurative "rib"), and makes a woman, Eve. They are then separated, instructed not to 'mix' with the other pre-humans, and then it all starts as we know it.

The question I often ponder is: what happened to all of the people then? Because chances are, the entire world was populated at this point. Well, I believe that two things happened: one, when God took his spirit away from the world, these pre-humans lost the guidance they once received - just like if you left a group of 7 year olds to their own devices. War, starvation, etc. probably happened. And whoever was still around at the time of Noah, were destroyed. The point is: I think Adam and his family were probably given strict instructions not to mix with them.

Side note: this mixing thing, I believe, happened with Nephi too. People like to think that the America's were empty when Nephi arrived; I don't think so because that's absolutely ridiculous. Yes, the Jaradites were destroyed, but I believe that's more of a reference to their society - and, their society primarily in that location. The Americas are a big place. So Nephi arrives and I believe that the Lord told them not to mix with the inhabitants, not because they were dirty or anything, but because there were more of them than Nephites. And if they mixed in, their culture and religion would have been gone within a generation; which is what happened to the Lamanites: they didn't follow the counsel and lost their religion.