In Naruto there is a group of abilities called Kekkei Genkai (血継限界). They are told to be "genetic" abilities which are (usually) passed down genetically within specific clans.
Notably, the eye techniques (Dōjutsu, 瞳術), such as sharingan, are also a subset of those.
How did those abilities first appear? Did they appear naturally, or were they made on purpose as a result of experiments?
Sharingan:
I'm guessing this would've appeared naturally, as with other Doujutsu (Byakugan and Rinnegan). Legend has it that these clans descended from the Rikudou's eldest son, who received his father's "eyes": his powerful chakra and spiritual energy.
Kekkei Genkai Ninjutsu:
I think these were developed by ninja who possessed special abilities and chakra nature affiliations. They were, later on, passed down on the next generations. According to this Leaf Ninja's page, they are creations indeed.
Potential Bloodlines and Genetic Advantages:
There are also Potential Bloodlines and Genetic Advantages, which also seem to be passable down onto the next generation, such as Suigetsu's and Mangetsu's body, which is unique to them and gives them a genetic advantage (I think these could've been the basis for the development of some Kekkei Genkai in the early stages of clans, though not in Suigetsu's and Mangetsu's case). I don't think they are considered Kekkei Genkai, but they could've been linked in early stages of development of a clan's special technique. I found out about these in this Leaf Ninja's page.
The Sharingan itself originated from the Ten Tails, he had what I like to call a "Sharinnegan", a Rinngean rippled eye, with Sharingan marks on each ripple.
The Sage of Six Paths inherited that power when he became the Ten Tails' Jinchuuriki, which was then genetically passed to his eldest son.
From my understanding, Sharingan is considered the Yin, while the Senju vitality and life force is considered the Yang. They are two halfs of the same whole, which is why a combination of the two can achieve the ultimate power.
Aside from that, "normal" elemental Kekkei Genkai is the result of a specific bloodline being born with two (or more in some cases) elements. This results easy manipulation and fusion of both elements, into the new Kekkei Genkai. These were probably learned/created early in the bloodline, and then taught to new members when they came of age.
There are also other Kekkei Genkai, like Kimimaro's bone jutsu, and Suigetsu liquefaction jutsu. These aren't explained in much detail, but they are probably some sort of genetic mutation which enabled their chakra to preform these techniques. Because it's a genetic mutation, only those bloodline members can use it.
There were expirments in Kekkei Genkai transfer and the results were inconclousive. It was seen that the Sharingan and even the Rinnegan can be succesfully transplanted and operated in the new host quite easily. However, when Orochimaru attempted to transplant Hashirama's cells into newborns, only one out of fifty survived and accepted the cells.
It seems that the first Kekkei Genkai was the rinnegan of Rikudo Sennin. Because he was the first ninja, I don't think that the Kekkei Genkai was an experiment, he literally "just had it".
Other Kekkai Genkais like the Sharingan are mutations of Kekkei Genkais (compare JNat's answer).
Maybe combinations (like Hakus Hyoton) are just mutations, suddenly appearing somewhere in the world.
I think they just appear. The reason why I say that is because of Kimimaro. Kimimaro came from a clan where no one had his kekkai genkai. (It was so vicious that his own tribe was afraid of him.)
His kekkai genkai just appeared. It's probably how most kekkai genkai appeared. I can't imagine someone "came up" with the Byakkugan or the Rinnegan. They're just genetic, like being really tall or really smart. They just are genetic combinations that run in bloodlines.
Kekkei Genkai is not something that is solely related to a technique, it is something that limits the other users to use the same technique to its full potential. We can say that it is the affinity of a clan to do the technique better and to improve it to further extent. You could use a Kekkei Genkai, but it will not be as strong and effective as it would be when done by a member of that particular clan" Kakashi had a sharingan but could not defeat Itachi as he did not possess Kekkei Genkai.
