Evolution
Evolution happens when a genetic mutation is passed down through several generations, and the species slowly changes throughout thousands of years. Typically, the mutation is helpful in survival, making it easier to reproduce and pass it on.
Natural Selection
Natural Selection is just the idea that some mutations are better than others. It's a messed up kind of survival of the fitest, the fitest being the animals that won the genetic lottery.
Artificial Selection
People hand pick different mutations and continuously breed them to make a 'perfect' animal or plant. This often messes up the animal or plant. An example of this is dogs. Humans bred different dogs, wrinkly skinned, longer dogs, shorter dogs, etc, to create new dog breeds. This is cool until your new dauchsund hurts her back or your old pug developes skin cancer. In other words, we should stay out of evolution.
Other notes
Sources
(Image from LiveScience)
(Image from National Human Genome Research institute)
(Image from Sled Dog Society of Wales)