Evolution is often used in an effort to try and disprove the existence of God. I often feel that doing so is like trying to prove that the sun doesn't exist because of one theory or another, when the sun continues to blatantly shine.
God exists. I know he exists. Personally, I know this because he answers my prayers. The scriptures explain that he reveals himself to those who honestly seek him, sometimes in person, but more often through the Holy Ghost:
"Draw near unto me and I will draw near unto you; seek me diligently and ye shall find me; ask, and ye shall receive; knock, and it shall be opened unto you." Doctrine and Covenant 88:63
I once saw a post where someone tried to refute that God answer's prayers. In his post he prayed "God, if you exist, appear to me right now!" and again "God, if you exist, give me a million dollars!" and then he went on to say that God doesn't answer prayers. If this petition were to me, and assuming I had the ability to both appear to that individual, and give him a million dollars, I wouldn't do either as well. Does this mean that I don't exist? I feel there is very poor logic in that author's comments.
But God does answer prayers. He certainly has answered mine, but I think it's important to have a correct understanding of who God is, if one is hoping to get answers. If a person were to label a rock with the name of deity, and pray to it, nothing would happen. Likewise if a person, like the author I mentioned above, thinks that God is an all powerful being who is somehow also desperate and willing to do anything for our attention and approval, that simply isn't the reality of God and, again, I'm not surprised if they don't get results.
Evolution and God
How does evolution fit, knowing that God exists?
To directly answer the question: I personally don't have enough information to say whether or not God created life on this world from simple organisms that he simply left to evolve into complex ones, or if he used a different method.
The prophet Alma explained that "all things denote there is a God," (Alma 30:44) which I would assume would include evolution.
Recently I was watching a presentation by a scientist who had spent many years searching for dinosaur DNA that he could use to genetically clone a dinosaur. At length he gave up, but realized that birds, being the long time descendants of dinosaurs, do have that DNA, but that over time the genes of their dinosaur parents had ultimately been repressed. The rest of his presentation talked about targeting the right genes to begin re-expressing the dinosaur traits.
I found it interesting that using the machinery that exists in our own bodies, we are learning to create different creatures by flipping the right genetic switches.
If we are capable of doing this, then what is God capable of?
Along this train of thought, there is a possibility to reality that I don't think some people may have taken into consideration:
Consider the following: Pretend you are born in a room without windows but there is a light. The light never goes off in the room because no one ever turns it off. You yourself are unaware that the light can even be turned off. As you grow you begin to gain confidence in your surroundings. You can recognize every object in the room and begin to feel good about your knowledge and mastery of all things that you are aware exist. Then one day, someone turns the light out.
It is the singular most scary event that has ever happened to you. Your world, not to mention your perception of reality, have just been rocked.
I mention this to bring up the concept that God's thoughts and ways are higher than ours. There could very possibly be natural laws, which God works by, that we don't even comprehend but that could turn the lights out on everything we have confidence in.
Is there any evidence that such laws could exist? The following isn't evidence, but just for example: Everything we know about the universe relies strongly on the law of gravity being in effect. This is a law that we know exists, but we still don't know how it exists, we just know that it does and we can observe the effect it has.
In scripture, there have been several instances where celestial beings have apparently not been affected by this law. If this same effect were suddenly applied to the universe as a whole, and gravity were to suddenly no longer be in effect, I imagine the impact it would have on our perceptions would be very similar to having the lights turned out in the room.
So I don't rule out the possibility that God just might have used laws that are greater than our understanding when it comes to the creation.
Evolution
In closing, I still think the study of evolution is important. I have found that because of our similarities with other living beings there is a lot that can be learned about the natural man that is useful in our learning to control it.
