First, before my lay explanation, you should watch this pbs doc. about the debate about "intelligent design" in Dover.
http://www.pbs.org/wgbh/nova/id/The scientists who testified explained clearly how evolution works and how there is a fossil record to prove it, etc. The IDers lost the case because their claims were unsupportable.. their "experts" weren't. There is really no doubt that evolution explains the diversity of life... no one has found any reproducible explanation for about a hundred years of trying. Believing a book of metaphors about a version of a god is not scientific proof and never will be. Evolution, however, does not discount any belief in god. It discounts a fundamentalist account of creation, that's all.
it's hard for us to imagine time as experienced by the earth. Think of a frog. It starts out as a tadpole with no legs or arms. Over the course of its development, it grows arms and legs, its mouth widens and it lives on ground and in water. That's quick time.
btw, it's imp. to note that it's not that "superior traits" beat out "inferior traits." There is no value judgment in nature. There are diff. habitats, and if you live in one you may die in another with the very same traits. When you talk about hybridization, you are talking about a "goal" for change. There is no goal for change in evolution, beyond an organism's desire to live and pass along genes. --but that organism doesn't get to decide what genes it gets when it is conceived.
Genes, in sexual repro., recombine into diff. variations. In the course of these recombinations, some genes mutate... they lose a chromosome or a gene gets left out and effects other genes.
The earth's climate etc. has changed many times over the course of geologic time... imagine a million years. Like imagining the billions and billions of stars in the universe.. An organism may be fine in one climate or place with x vegetation, but then climate or veg. drastically changes. The organisms that have mutations that made it possible for it to survive in the new climate get passed along to their descendants... whose genes also mutate. And then, maybe another climate change makes a big difference in those descendant's ability to survive and mutations again may make it possible for some to survive.
A million of years of this.
Then, a group of... pony-like animals gets separated -half and half on one side of a crevice. Their genes don't mix. All still have mutations, but they no longer share the same gene pool, and one may adapt to one climate while another adapts to another... they travel away from each other in search of food. Hundreds of thousands of years of this... and one is a horse and the other a zebra.
Where are the not quite humans? Are you familiar with anthropologists who have found bones of pre-human ancestors? Like "Lucy" the australopithecus? There are hundreds of fossils that establish change over time... skull size changes, teeth for one kind of food vs. another.
There was a great program on PBS tonight that demonstrated that apes (common and bonobo chimps, gorillas) could understand humans who talked to them. They performed tasks when they were asked, while the one asking had on a helmet that covered the face (so no prompting.) It was amazingly beautiful. If you look at the genetic make up of chimps and humans, we're not that different. However, the ancestor that was the basis of their mutations to them and our mutations to make ours separated at some point and habitats changed and made chimps chimps and humans humans.
If you had not heard about creationism growing up, and had not associated it with a belief in god, this is very easy to understand, even if my explanation isn't the greatest.
again, watch the video above.