1) WHAT SUSTAINS THE SYSTEM? Magic? Age? Customs and traditions lost in the mists of time? Religion? Blood? Inertia? A combination of all or some of the above plus other factors? (I personally think authors, especially fantasists, underestimate inertia as a social force. Sure, there will be people burning for more than they're given in every society, but there will also be plenty of people convinced that all they need is right here, and at most they want to make a few minor changes to ensure their own personal happiness).
Once you know what holds the system in place, you should have a much better idea of how the classes or castes interact, what small outlets for steam and change are permitted (see point 3), what the points of contact-and slippage-between castes and classes are, how they act internally (see point 4), how conscious people are of it (there's going to be a difference between power constantly reinforced by flashy displays of magic and power that has sunk into the fabric of everyone's everyday lives to the point where most people don't notice it anymore), the age of it, how extensive it is (see point 2), and so on.
If you don't have the slightest clue what sustains your class/caste system, I suggest you find out. About now.
2) WHERE DOES THE SYSTEM STOP? Sometimes it ends at a nation's borders, but sometimes not. For example, caste systems of some sort or another prevailed in many of the Spanish colonies in the New World; the "pure" Spanish were on top, the "pure" Native Americans and Africans were on the bottom, and in between were all the various possible combinations, with different positions depending on which color which parent was, how rich a Spanish parent had been in Spain, how long ago the mixing of "other" blood had been, what language a person spoke, where they lived, how great their chances were of actually leaving the colony and going back to Spain, and so on. The system stopped, for obvious reasons, at the ocean, and did not cross over to Spain partially because Native Americans and Africans were rare enough in that country not to make it necessary. (Spain was also the only European country to have been conquered by the Moors for centuries, so that perception also influenced the way the "hidalgos" and "conquistadors" responded to people around them in the New World. Not to say that Britain, France, and Portugal were much kinder).
Other times a system might extend across cultures, say if you have classes substantially established in a home country and then carried to another by colonizing powers-and then the natives in that area are weak enough not to become a major factor in altering the system as it reestablishes itself. This was the case of many British North American colonies where the Native Americans were weak enough to provide, at most, a feared or admired enemy on a few occasions, but the colonists were more concerned with their own internal affairs and their relationship to the colonizing country. (Disease had given them that luxury). It's not to say that the people involved have to recognize what they're doing, or end up replicating exactly the same relationships; the United States has famously been a "classless" nation.
Know what limits the class/caste system, whether it's bound to place, culture, society, or a mixture of them.
3) KNOW YOUR VENTILATION SYSTEM AND YOUR CARNIVALS. What are the outlets, the places where the steam and the anger of those who suffer within the class or caste system can leak out? They might be carnivals, or days when the master and the servant switch positions (as April Fool's Day sometimes used to be), or the acceptance of a few "talented" or "special" or "unique" individuals who rise up the ranks and so become less dangerous when they're at the top. If the dissatisfaction is widespread, it might erupt into riot, revolution, or civil war, but any class or caste system that has lasted generations will have mechanisms in place to help prevent that from being the inevitable reaction.
This is a good place to consider what exactly the place of social mobility "is" in your world. Is it accepted for those few talented or special individuals? (A deeply cynical part of me wants to write the story of the peasant hero who becomes king from the point-of-view of nobles who decide that he really has aristocratic blood against all the evidence, because that's the only way they can accept someone from a lower class ruling over them-if he's "really" one of them. This is also why I want to drop-kick authors who reveal that their "ordinary" person actually has the blood of kings or gods after all. Even urban fantasy has its variant, where the "mundane" heroine turns out to be descended from fairies, as if it doesn't make sense for her to have achieved her victories on her own). Is the mobility denied, but happens anyway under the covers? Is it considered possible through a mechanism that no one has ultimate control over, like reincarnation, destiny, a god's favor-possibly someone could fake this-or the sudden choice of sentient magic to hang around a certain person? Does it happen without existing as a concept, so people who rise from one class or caste to another don't conceive of themselves as part of a process that others can access? And what about downward motion? Can you commit a sin or crime or loss of fortune that makes you Erzenkangran where you had been Ezzeran? If you have children with someone not of your caste, whose standing do they take on? (In British North American systems of slavery or indentured servitude, it was usually the mother's; the child of a slave woman was not born free). And how many people are incapable of accessing whatever mechanisms for social mobility or softening the blows of the system exist, and have to stew their lives away in helpless frustration and anger?
Those stories of frustration and anger aren't ones I see often. And while the people who are "special" enough, and potentially troublesome enough, to rise are great, I'd like to see stories of endurance, survival, and coping, too. Or people who can rise, but don't take that as permission to cut off every human connection with the characters around them who aren't as lucky.
4) WHAT IS THE INTERNAL REALITY OF EACH CASTE OR CLASS? Again, most fantasy is slanted. We get to see the internal reality of the highest class, or the royal caste. We know how they think of themselves and how they interact among themselves as well as what they think of others below them. Yet when lower-class characters appear, most of their energy seems to be taken up hating or adoring those above them, so the whole story is nothing but a mirror of a mountain peak. We rarely get to see the lower-class people interact with their own families, friends, and neighborhoods. We don't know how they think of themselves.
So, consider. What kind of internal realities "does" the class/caste system you're working with create? They might be pleasant, but try to explore the unpleasant ones, too. And know what the context-in this case, the system and the forces that created it-might make pleasant and unpleasant for different people.
And that means including both mental "and" physical conditions. When lower-caste characters do appear on their own merits, they can starve, have sores or diseases, scream and bleed, hold starving and dying children-but we don't get to hear them think or speak. So feel free to contrast material conditions, but try to take on their personalities. (See point 7)
5) REMEMBER THAT RELATIONSHIPS ARE MORE COMPLICATED THAN JUST "TOP" AND "BOTTOM." If the class/caste system you're building is immensely complicated-the way it often was in the Spanish colonies-then the extreme top and the extreme bottom aren't the only ones that can interact. Take a family with five siblings, and the youngest and the oldest don't just relate to each other; they have their own relationships with the middle child and the second and the fourth. A system with five castes or classes should do the same thing. Meanwhile, all the ones in the middle have their relationships with everyone else, too.
How do they think of each other? How do they react to one another when individuals meet? How often do they have "occasion" to interact? (How far apart do the different classes and castes live? Even in large cities, classes often separate themselves). What stereotypes (probably more important than realities) exist in the heads of people from certain classes/castes as they think of other classes/castes and govern their reactions? What narratives do they tell about each other, and who gets to imprint the narratives as more than stories on the behavior of others? If there's a crisis-a war, a famine, a plague, an alien crash landing-who's the cannon fodder, who's the scapegoat, who's the protected and cherished victim?
And how often do they get to break through and see individuals?
6) KNOW HOW CLASS AND CASTE INTERACT WITH OTHER FACTORS IN THE SOCIETY. Among those, but not limited to them:
-Gender.
-Age.
-Race/ethnicity.
-Occupation.
-Religion.
-Politics.
-Economy.
-The legal system.
-Nationalism (if it exists in your world) or identity politics of other kinds.
-Art.
-Culture.
-Science.
-Mythology.
-Physical realities of the world (hunger, thirst, disease, need for shelter, cleanliness, geography).
-Magic.
-People's sense of themselves as individuals.
-Other narratives that may oppose the class- or caste-bound one.
Even if your system is based on one or more of the above-if it has rankings based on who acts more masculine and feminine, for example, or if the most powerful mages rule, or if religion has dictated that certain people are pure and holy while others are not-it is not "identical" to those things; there can certainly be aspects of gender or magic or religion that the system names only vaguely, or not at all. I think one way that a class- or caste-based fantasy can fail is to assume that this system is the only defining factor in everyone's lives (it never is; if nothing else, physical realities have got it beat). A second way is to assume that it only acts in isolation and is utterly immutable, and nothing can challenge, change, modify, or bend it. Point 3 gives one example of why that's not true; that list up there is another.
This is another recipe for enormously complicated fantasy, I know, when perhaps you wanted to write a simple story about a three-tiered class system based on magic that the protagonist travels on a picaresque journey through. Sorry. I appear to be incapable of not leading it back to complication.
7) THINK YOURSELF INTO IT. This is a place where a deeper sort of body-centered writing helps. Normally, I think body-centered writing depends on trying to "feel" what your character does, "see" what she sees, try to imagine what it really is like to climb down a cliff or ride a dragon. For a fantasy with a class or caste system wildly different from the society you live in-and this only gets more urgent if your class or caste position is not particularly important to you-try to think of the character's body and mind as a citizen of that system would think of it.
If women of a certain caste are considered violently ugly and unclean at all times, but it gets worse when they're menstruating, then try to imagine how a female member of that case would feel when she starts bleeding, and how she would think of herself. It's not pretty, but it's necessary, and it's probably the best route to avoiding caricature and exaggerated reactions that, once more, will make the lower-class character into a stereotype while leaving the higher-class observer untouched.
If your character is on the fringes of her own class, in an occupation that makes her have to deal with those of other classes a lot-say, a dressmaker to fine ladies-she might need to be exquisitely aware, at all times, of what clothing and look and posture and tones in the voice suggest. Think like that while you're writing her. Deciding it's not important because it's not important in your own life creates falsehood, again.
If you say that your system encourages citizens of certain classes or castes to think about their minds and bodies in certain ways, then "show it doing so".