Unless you have some sort of hivemind or telepathically dropped link (and sometimes even then), you will have variations in the ability of people in your culture to access education. People might theoretically have equal access to all information, but someone with a drive to learn is going to access a whole lot more simply by their choice alone. When thinking about access to education in fantasy worlds, consider not just what is societally available, but also the motivation of the characters in question. How much education do they want to access?
Who can access education?
Are all people allowed to access education? Typically, all people will have access to some level of education, even if it is no more than what is needed to follow orders and recognize their superiors. But you may have classes of people who are viewed as sub-human or animal in nature, and are barred from the education given to your average member of society. In such cases, what education are they openly given, and what do they trade within themselves?
That said, even for an average member of society, there may be barriers to accessing any more than the very minimum level of education. If everything above the basics is taught in distant schools, then people without the means to travel there won’t have access to it. If the student must pay for education, then poor students won’t have access to it.
Education might be intentionally restricted by guilds or other such societies. Traditionally, guilds kept the knowledge of their professional skills secret to prevent competition. Or, you might have religious secrets that are only accessible to those who move up the ranks of the priesthood.
If magic is believed to be something innate (whether it is or not), magical education might be restricted to those who show the appropriate aptitude. Conversely, a society might make a show of magical education being “available for everyone,” while in actuality it’s only available for an elite few, or those who do have an innate talent.
When considering access to higher levels or specialties in education, consider prerequisites. If someone wants to study to be a teacher/priest/mage/bard/hunter/etc, what skills/knowledge do they need to have ahead of time? How does one obtain those prerequisites? Can they be waived for certain people? (Think of the privileges “Chosen Ones” and people with family connections tend to get.) Are extra requirements added for certain people? (Consider the extra requirements added for Kel in the Protector of the Small quartet.) Extra requirements are ways of weeding out people who are technically acceptable but socially unwelcome.
Are there literal barriers that appear when one tries to access education? Think of a school that is hidden in a labyrinth, underwater, behind a magic veil, or up a mountain. Think of the mundane accessibility problems from those who have to use crutches or wheelchairs to get around. Could you imagine trying to use a wheelchair on the moving staircases at Hogwarts?
Do different levels of education correspond to different social classes?
The answer to this question is dependent on how the social classes are divided in your world. Money is the most basic division and will affect just about every culture that has a moneyed economy. But people could also be divided based on citizenship, gender, magical ability, species, ethnic group, religion, etc… People who conform to what the society at large values (the correct religion/appearance/gender expression/etc) are more likely to have more access to education (and other forms of power) than those who miss the mark in some way.
Education that has to be paid for will vary greatly depending on wealth. The wealthy will have far more access to education than the poor.
To take a look at something most people tend to gloss over–how are the outcasts of society educated? Outcast is a broad term that can cover anything from the untouchables to the homeless to social pariahs, depending on how your society is structured. If a child is born among the outcasts, what sort of education do they have access to? If someone becomes an outcast later, are they allowed to continue their education? Is it even safe for them to do so? Depending on the complications that made them an outcast, is it even possible?
What education do the outcasts share amongst themselves? Do they teach each other to read, to do math, do practice magic? Do they tell the new outcasts the best place to find a free meal, or an overhang to shelter from the rain?
Is there any knowledge that is zealously guarded within any particular social class?
How is access to education related to gender norms and family responsibility?
Who is expected to go to school to get a better job? Who is expected to stay home and take care of the family members who need it/take care of those going to school?
Are children expected to get a good education so they can get a good profession and take care of their parents? Are the oldest children expected to get a job immediately after basic education so that the younger ones can continue on? How does responsibilities in families shift between the size of family, the profession(s) of the family, and the health of the family members?
One of my close friends was expected to (and did) get a job immediately after graduation and start working to help put her siblings through school. I knew many women in both high school and college who dropped out of school upon getting married.
If food/meals are something that takes many hours to prepare, who is taking the time to prepare the food instead of being educated or otherwise working to support the family financially? How many people are needed to support a family financially? Does that number change depending on how educated the individual workers are?
Are the genders divided in their lessons? How does this affect those who don’t fall neatly into the gender binary? Are particular genders expected to be better at a certain subject? What happens when someone from gender A is good at the subject expected out of gender B? How do the expected subjects of excellence relate to later professions and gender expectations/roles?