Life is built on information, contained in that molecule of heredity, DNA. Dawkins believes that natural selection and mutations (blind, purposeless copying mistakes in this DNA) together provide the mechanism for producing the vast amounts of information responsible for the design in living things.
Two fish are better at swimming than most other fish. They're both the result of the combination of one parent with a strong tail but poor eyesight and one parent with good eyesight and a weak tail. They both ended up with the good tail and the good eyesight (while their siblings ended up with other combinations). These two fish get lots of food, avoid predators, and eventually find each other and mate. Their children are now going to be at least as good at swimming as their parents. Maybe one of them gets a favorable combination of bone structure or additional muscle potential from the parents that they hadn't fully developed - and that child is better at swimming etc.
Through several generations, natural selection favors the most suited to the environment. Predators, disease, and anything that causes death interacts with the fact that genetic information is shared between pairs differently for each offspring. In society, you see one child that ends up with red hair and think nothing of it. In the fish world, that color variation just might blend in with some coral enough that it gives that one child - that one combination of genes, an advantage over other children.
03R1
Natural selection is a logical process that can be observed. However, selection can only operate on the information already contained in genes — \ it does not produce new information.
That's true. Natural selection does not produce new genetic information. It only selects out certain offspring, thereby directing the course of genetic evolution in a particular species.
Human beings are currently in a state at which we still share genetic information, but we no longer suffer natural selection (much). Almost nothing kills us off before we reproduce. The things that do kill us off still play a role in natural selection, but most of the diseases we face, and traits we carry don't manage to get us killed before we have children. That's because we don't have bears or mountain lions picking off the slow ones anymore.
Edit: I've said this before in this thread, but I think it bears repeating. Why do you like the looks of a lush forest? Why do you think that snow capped mountains, waterfalls, and oceans are beautiful? Why is it that you think flowers are attractive, or that babies are cute? All of these give you an advantage in the wilderness. Lush forests have lots of food and places to hide. Snow capped mountains, waterfalls, and oceans all have one thing in common - water (where there's oceans there's rain, rivers, fish, etc.). Flowers grow where there is water in the soil and an abundance of fruitful plants. Finding babies cute ensures that their mothers aren't going to abandon them.
All of this could be explaind by saying that God thought about all of that and made us that way on purpose to give us an advantage in the wild. But it makes more sense to suggest that these sorts of traits/interests/preferences developed because the people that had them survived more often than that some creator took into account every single one of these details and designed us that way. Otherwise, wouldn't men find babies cute too (more often that is, I know some of you do)? Wouldn't we care a little more about the feelings/well being of other men? These things don't confer an advantage in the wild, which is why we don't have them, but I'd think a divine being would think of those things and hook us up.
In general, just about everything wrong with our species is evidence that we were not designed by God, but instead designed by predators and disease.