This isn't that hard to understand. As I mentioned, unless the recipient of a positive mutation ALSO has no major negative ones, then the positive mutation will not be passed on as the creature will not be more fit than its competitors. The vast majority of mutations are negative, but these aren't passed on normally because, in nature, being less competent will be the result of negative mutations. This is why evolution takes hundreds of generations to produce major change in wild species.
Humans and domesticated species are different in that natural selection is almost always replaced by artificial selection, in which mutations that produce desirable traits are chosen over those that enhance survivability. Humans have for thousands of years been so secure due to the safety of civilization that what looks good is chosen over what is evolutionarily beneficial. An example would be blue eyes (much greater chance of vision loss than brown) and as a result, many mutations have built up in our species' genome over time. In domestic animals, humans breed animals with traits they like together, such as a certain fur color pattern. Frequently animals were bred together that were closely related to effect this, as they have similar gnetic make ups and are far more likely to both exhibit the same trait than individuals that aren't closely related. But, as you should know, breeding close relatives also greatly enhances the likelihood of bad genetic defects, which is why, for example, dalmations have beautiful spotted coats yet also are prone to horrible genetic illnesses.
So to recap:
natural selection = positive mutations promoted, negative mutations selected against, ultimately resulting in a more fit species
Artificial selection = mutations that produce desirable traits promoted (often through breeding close relatives) ultimately resulting in a less fit species