I Was going to edit this into my previous answer, but there are three reasons as to why I think it should stand alone:
- The indirect nature of the evidence
- Length of post
The first examples used here are taken from the 1988 Superman CBS cartoon series (one of the BEST examples of the hero in animated form, in my opinion.) The last 5 minutes of each episode would be dedicated to a segment called Superman's Family Album, in which the show would present stories of Clark/Superman growing up at different ages and going through different childhood milestones in Smallville with his parents, the Kents.
Though this cartoon was made after the Jon Byrne 1986 reboot of the character.... where Clark is basically a "slightly enhanced human" until he absorbs yellow sun radiation and "grows into his full powers" in adulthood.... this version of the story balances both the Post and Pre-crisis versions of the character, combining aspects of each and simplifying them.
Post Crisis Aspects:
The (then) modern-day aspects drawn from Byrne's version include:
Clark doesn't become a hero until he is a fully grown adult in Metropolis
Superman is more a "public face", but it's the "same guy" (Clark Kent) doing what he feels is right
While godly powerful, he's not infallible, or invincible, even against some human tech.
Little is known or made of his life on Krypton before coming to earth, and by all accounts, he is the "sole surviving member" of the planet (no Kara or Superdog seen.)
Both of his parents are alive in his adult years, and act as a humanizing/balancing influence, as well as his secret keepers and occasional helpers.
His main foe Lex Luthor is more "stylish 80s corrupt brilliant publicly respected Business man" than "maniacal super genius mad scientist and world renowned villain."
The more throwback or classical elements that were kept in this superman were:
He's TRULY Super, able to move landmasses, moons, if not whole planets, with ease, shrug off lightning bolts, survive in space unaided, move at light speeds, and even has a form of tactile telekinesis (in the Cybron episode he managed to keep himself, Lois Lane, a table and 2 chairs afloat in the sky without "flying" for her birthday.)
He knows a lot about Krypton's history, and even this version of Zod seems based around the classic 1950s design.
He is NOWHERE as "conflicted" in himself as Byrne's version, having the whole "Big Blue Boy Scout" and pleasant demeanor of the Christopher Reeve version.
His exaggerations of Clark Kent as being somewhat nerdy, awkward and "mild mannered" are used to distinguish him from Superman, with even their voices being portrayed differently by the same actor.
While not as wild as the Superboy/Superbaby stories of the 1950s and 60s, Clark's parents do have challenges protecting his secret as a kid, and influencing his decision to be a hero in the future. The last episode even shows it was his mother who made his suit "out of the baby blankets he came from Krypton in," making the suit itself as invulnerable as he is and bypassing the "bio-electric aura" excuse for his indestructibility.
Most notably for this post, while he never had a career as Superboy, let alone a "super baby," Clark did have FULL KNOWLEDGE of, Control over, and USE of ALL his powers, even as a child. This included everything from invulnerability and flight to seemingly super intelligence... or at least better understanding than any other child that age.
This last point becomes important, because it implies, as the previous answer did, that Clark knew full well from babyhood that his parents couldn't "force him" to do anything he didn't want to. Despite this knowledge, he willingly not only followed their orders, but chose to do so.
As the question basically asked how the Kents "raised a super baby," we have no example of direct means (like physical control, mental manipulation, bribery, etc) used outside of Martha Kent's stern voice and balanced caring, responsible, reasonable concerns. There was no "special method" per say; she set rules, and he followed them, exampled in the video by her teaching little Clark to be careful about his powers as "our little secret."
However, both of the clips provided show that, even though (like any young child) Clark could be willful, emotional and prone to occasional mischief, he was smart enough (and instinctually respectful enough of their parental authority) to never break the rules too heavily. This implies that he basically "allowed them" to teach him right from wrong by purposefully following the examples his human parents set. This seemed to be the case, even as a child presumably under a year old.
This first video, "the Adoption," shows Clark, as an infant, essentially choosing the Kents specifically to be his parents.
Not only did Clark actively scare off the other people that came to consider him for adoption, but the kid..... who is not even old enough to coherently talk at this point.... flew directly to the Kents' farm and settled in with them. And you see that look he gave at 1:17 when the first couple came by? That boy hadn't been on earth more than a few days, yet realized exactly what he was doing! Even the director of the Orphanage himself said it in the episode:
I tell you, Conroy, it's as if the boy was TRYING to run those people off! Maybe he wants someone else to be his parents; I don't know...
This implies Clark had
(1) the above average/ super human intellect to discern the problem he was in, as well as
(2) the intention to be SPECIFICALLY with the Kents right off.
Whether Clark had just "imprinted" upon Martha and Jonathan as the first humans he saw when he arrived here, or there was some "destined" element or psychic link, is unknown. Either way, Clark made a decision to be part of that family, and in the ensuing years, despite being faaaaar more powerful than they were, he obviously also made the continuous choice to abide by their rules.
The second video, "The Supermarket", shows this willing obedience more clearly.
Here, Clark is a toddler of about 2 or 3 years old, and like most kids that age, he's impulsive and a bit precocious. Being so young, he doesn't quite grasp the whole "don't use your powers in public as it is not normal and will draw attention to us" thing yet... but he did promise not to cause his human mom any trouble. Aside from following a few kiddy impulses regarding food, he did obey her instructions without much contradiction. Beyond that, like most kids of that age doing something new, he was excited and sought to be helpful to her where he could. This again goes back to a combination of his intelligence, his basic good nature, and his willingness to do everything the Kents taught him to do... even if they couldn't effectively "punish him" as most parents could with other children.
Jonathan and Martha Kent having a pre-existing "connection" to Clark, or being deemed worthy to be his parents has been touched upon in other forms, as well; as User 31178 pointed out, in the Smallville continuity----- one which, oddly enough, has arguably the most interaction of Clark with his human parents in showing how they raised him ----- it was stated outright in a season 1 episode where they weren't scared of him, and they rarely had any problems out of him as a child.
A season 3 episode touches on this further; it shows Clark's biological father, Jor El, came to earth several decades previously, as a sort of right of passage, and actually met up with and befriended Jonathan Kent's father, Hiram. Hiram told Joe (Jor El) who had been falsely accused of a murder that, "if you ever need anything, you know where to find me." Clark literally "sees" all of this via a type of telepathic journal amulet his father Jor El left behind in the Kowachee caves. At the end of the scene, Clark himself tells his human father, Jonathan, that "I don't think I came to you by accident. I think you were chosen."
If this is the case...that the Kents were purposefully chosen to raise Clark as they were deemed capable of giving him the foundation of character he needed.... then that reasoning may apply only to the Smallville universe specifically. However, as most versions of the hero has him being raised by the Kents, the canonicity of this theory could be somewhat speculative.
There was a book several years ago (firmly set in Pre-crisis continuity) that had Albert Einstein be contacted by a telepathic scouting device from Jor El prior to Krypton's destruction. As it recognized Albert as having the "greatest mind on the planet", the scouting device tasked the scientist with "choosing the best possible candidates" for the responsibility of raising a child who could change the world. Through and the scientist then sought out the Kents.
This was done from the 1981 Elliot S. Maggin book Superman: Last Son of Krypton. Excerpts can be read here
"My name is Jor-El and I am speaking to you through the use of a device which relays spoken information directly into the mind of the individual it contacts. My recording is incorporated into a navigational device whose purpose is to lead my son Kal-El to a planet by intelligent creatures whose thought patterns roughly correspond with those of the humanoids of my planet, Krypton. By the time you receive message my world will have been long destroyed by natural forces. Since the cataclysm, my infant son has been traveling through space at a speed close to that of light, and the time has passed for him slowly enough so that he is just beginning to feel the effects of a day without food. At moment he is slowing down in preparation for entering your field of atmosphere.
"Just as the navigational device was drawn to a world of intelligent beings, it was drawn to you, the most highly developed intellect on your world. The purpose for is to implore you to take in my son Kal-El as your own and see that he is raised to proper manhood. "
The point still stands, though: The Kents managed to raise the alien child either because Clark himself "went along" with it, or because some other Kryptonian influence reasoned that their characters were strong enough that Clark would willingly obey them, even with the advantages he had over them.
Now again, these are TV shows I'm referencing, so their canonicity could be subject to question, but at the very least in their respective Superman universes, it's shown, if not at least implied, that there was some conscious decision making involved in how they managed to raise Clark, either by the child himself, or by some other , more knowledgeable force, and that this was due to them being the kind of good people that Clark could be naturally influenced by.