Questions on Natural Selection

I have a question about natural selection for those who know how evolution works.

I think I understand the general idea: The fit survive and pass on their genes, whereas the unfit die. For Richard Dawkins, that accounts for much of the apparent "design" in life. In his view (as I understand it), I as a human being have (say) an eye not because God designed it for sight, but because only those with eyes were able to survive and reproduce. Fit animals exist because they were fit enough to survive and pass on their genes, not because God made them fit. That's my understanding of natural selection (which may be flawed).

My question is this: How did the fit become fit in the first place? Was it through a random mutation? I know that nature weeded out those without a functional eye, but did the eye itself emerge randomly, according to evolutionists?

Creationists and advocates of Intelligent Design argue that an eye needs all of its necessary parts in order to function, so it had to be created whole at the outset. Otherwise, all of those creatures a long time ago would have died off because of their deficient eyes, and there'd be no life right now! Michael Behe refers to the analogy of the mousetrap, which needs all of its parts to work. For Behe, a mousetrap in which one part is deficient cannot do its job, so it makes more sense to say that someone created the mousetrap in a complete and functional state than to suggest that it evolved there through imperfect stages (in which it wouldn't even work).

Critics of ID counter, however, that an imperfect eye (and an imperfect mousetrap) can still be functional. My question: how does the imperfect eye become more functional? Is it through a random mutation?

I can understand that the fit survive, but is there an evolutionary answer for how the fit got their fit characteristics in the first place?

Rule: Please address my question without calling me ignorant!