First, there is one thing all major religions have in common. Complexity. Religions have multiple layers, multiple purposes, multiple actors, multiple sources, and these all interact and change over time in response to both each other, changes in society, cultural influences, individual people of influence, political events... Any image of religion is going to be partial, fragmentary, and contradictory.
For example, a major religion would probably have following elements.
A religion would probably have established canonized scripture and established dogma. These would have been written at different times by different people having different opinions. Overtime the cultural, linguistic, and dogmatic differences between the writers and readers will accumulate and interpretations will vary over time and place, and almost certainly lacking serious scholarship and research be quite different from originally intended meaning.
Yet while interpretations vary, possibly to the point of religious war, having authoritative writings gives religion continuity and stability. Drawing a line between orthodoxy and heresy based on commonly accepted canon protects religion from disintegration from transient political concerns and local differences in belief.
Clergy needs to be trained and administered. Places of worship need to be built and maintained. Rituals must be formalized and organized. Dogma needs to be defined, interpreted, updated, and defended against heresy. Political aspects of religion must be handled.
Religions do not exist in a vacuum and religion has lots of power over the minds of people. Somebody needs to make religion compatible with the other power groups such as kings, nobles, mages, merchants, and guilds or eventually lots of people will die. Sometimes quite painfully. This happens both by reinterpretation and redefinition of dogma and by influencing other groups to accept the proper religious authority.
Religion is powerful agent of social identity. People identify very strongly with their religious community and will go to great lengths to conform to the values and expectations of their community. This is a major component defining the moral and ethical values of the people. If people believe their religion condemns some practice, people practising it will be stigmatised and even punished. If people believe their religion approves of something, they will approve it as well.
It is the task of the common clergy to keep the beliefs of the people within accepted dogma and prevent heresy and religious division. They often fail. What people believe generally differs from what the clergy teaches. Which differs from the current dogma. Which in turn differs from what the canonized texts actually say. Usually this will stay within acceptable limits, but this is sometimes achieved by widening the acceptable limits.
People will have beliefs and rituals they did not learn from clergy and that the clergy may even condemn and try to remove. This may be remnants of previous religions, superstitions, or local interpretations of the main religion. Or simply traditions. In a world with magic they may even be old pacts with local spirits. Or Old Gods.
These folk rituals and beliefs will blend with the official religion and give it a rich texture and depth that a religion dictated from above would lack. Sometimes the beliefs may become so popular the end up affecting the official dogma. After all even a great religious leader will still be affected by the beliefs and values he had as a child.
A truly successful religion must not only be able to affect the values and mores of communities, it must also be able to touch the hearts and minds of individual people. When a person searches for greater spiritual or ethical depth, he should be able to find it from his religion. Otherwise apostasy will spread and the social elites will become secularized.
There are rarely one size fits all solutions to personal religious needs and a major religion will usually have multitude of sects and orders to fulfil the spiritual needs of the faithful. There will also be a multitude of various schools of thought within the faith that have differing theological and ethical interpretation.
Usually personal religious beliefs will be tolerated by the religion as part of the personal relationship the faithful have with the faith. But sometimes people of deep faith cannot tolerate the mainstream religion and become heretics, apostates, or reformers. Even prophets.
This is one way to see the structure and organization of a religion. You should remember that while all these elements are connected and create a whole, they also evolve separately and respond to different forces. A political change might cause a fast change in the dogma and organization of the religion to match the new reality. But at the communal level the same change might take a generation or several generations. A conservative religion might fall out of touch with the personal and communal beliefs of the faithful.
Different communities might have quite different and even incompatible views of the same religion. Usually religious authorities will try to suppress such differences. Some differences will be deemed harmless and will be tolerated. Sometimes it will be more profitable to let the differences grow and then cut off the cancer with sword and flame. Sometimes this fails and schisms happen. Some schisms are temporary some will create permanent divisions.