I think I've found a really good way to explain natural selection to kids, or their intellectual inferiors, the creationists (Just kidding, just kidding). Take a look at this site. Go to the game in which you can play as a bird eating the pretty peppered moths. Start gobbling them down! As you'll notice, at the end of the simulation, there are a lot more moths which match their backround (in the light forrest you end up with mostly light moths, in the dark forrest you end up with mostly dark moths). Think about how this applies in real life: In real life, the moths that had a survival advantage (matching their backround) would also have a higher chance of making baby moths, since you have to be alive to make baby moths (duh!). In the dark forrest, the dark moths (on average) will leave behind more offspring because the dark type survives more often than the light type. The children of the dark moths will usually inherit the coloring of their parents. Since the dark type is constantly becoming a bigger part of the population, eventually the whole moth population is dark. The takeaway lesson: A genetic change that helps an organism survive longer will usually be reproduced more until it is present in the entire population.
Now, creationists may scoff at this, calling the original peppered moth experiment flawed. But the moth experiment was redone, and with the results expected.
Nor can creationists say that mutation and selection don't produce complexity (or 'information'). I've debunked that claim numerous times, Just search my blog. Or watch this video that explains the evolution of the eye. And remember: At each stage of the evolution of the eye, the new stage (accomplished by mutations in the genome) becomes common because it gives the organism a better chance at survival. As we saw earlier: A genetic change that helps an organism survive longer will usually be reproduced more until it is present in the entire population.
Incidentally, the peppered moth evolution is also a good teaching tool for when someone asks, "If we came from monkeys, why are there still monkeys?" Of course, we didn't come from any species that's alive today, but we do share a common ancestor with chimps, gorillas, orangutangs, and so on. But humans did evolve from a creature I think we could call a monkey: We evolved from a primate that walked on all fours and was very hairy. So why are chimps and humans different? They were in different environments with different selective pressures (The selective pressure is the environmental condition that favors certain genetic changes over others). Go back to the moth simulation: Try out both versions. Go to the light forrest and then the dark forrest. Notice that in the light forrest you usually end up with mostly light moths. In the dark forrest you usually end up with dark moths. The populations are different because the selectve pressures are different: In the light forrest, the selection pressure is for light moths, and in the dark forrest, it is for dark moths. Back to humans and chimps: Human ancestors lived in different environments with different selective pressures than the chimp's ancestors. That is why they are different.
Now, if one wants to see the actual evidence that all living things evolved from one (or a few) original species, here's some material on the web that you can look at, and here are some books you can read.