I think the advice that says politics is about power is good to consider. However, I would add that it isn't just power for power's sake. Power is energy. If it isn't doing anything, it is only potential--something to account for, but not something that is having an active effect on the world. Politics is kinetic or power in motion.
Power allows its wielders to accomplish one of two goals: secure their autonomy or enact their agendas. These often, but don't always, go together. Sometimes, when they diverge, it depends on the source of the power. Note: Autonomy isn't just freedom, but is also the ability to meet your own needs.
For example, two students go to university; one cooks his own meals and the other eats in the dining hall each day. The latter has paid for convenience and possibly for more time to devote to her studies (fulfilling an agenda), but the former has more personal autonomy. If the dining hall suddenly shuts down, he won't be going hungry.
So, since sources can affect how power is used, I think it is most important to start with those.
Some major sources of power are
- tradition
- religion
- wealth
- political structures (e.g. a constitution)
- access
- influence (both broadly/culturally and singularly/personally)
- fear
- might
- knowledge.
It is important to know how each source grants/uses, limits, and revokes power. By grants/uses I mean what are the ways a person can wield the power of the source? In political structures, one way is laws. In influence, one way is a whisper campaign or advising a friend. In religion, one way is declaring something anathema so that adherents avoid it. Each power source determines, to a degree, what a person can do with it. Most people and organizations cultivate multiple sources to widen their menu of actions and to compensate for limitations.
For example, wealth grants power by enabling the wielder to convert the wealth into a different type of power.
For example, they can buy off a priest for religious power or they can spend to be on the edge of trends for influential power. They can cultivate a salon of innovative ideas for both influential and knowledge power. The power of wealth only lasts as long as the money holds out, however. Anyone relying on wealth will find themselves powerless when the money goes, unless they've, for example, collected blackmail (fear-based power) or connections (personal influence; being someone others listen to). Another limitation is that power bought by wealth may carry the stigma of money (e.g., they bought their way in, etc).
Another example, political structures may elevate one person as ruler over the land, but they are limited by the description and responsibilities of their role. They may also need to work with other entities created by the same political structures. Many leaders cultivate another power source to ensure they can enact their agendas (e.g., influence, tradition, religion).
Also, note, no source is infinite. The fewer who draw on a source, the more power they have.
The next step is identifying who in your setting has power and what kind of power they command. Guilds have knowledge power--they're the ones who know how to do crafts. They may also have access power aka the decision of who gets to learn the craft. That access power could also belong to the local government, church, etc.
So, figure out who the players are and what kind of power they access.
Next, going back to the top of this post, think through what each player wants to do with their power. Is their focus fully on remaining free from any strictures and being able to meet all their needs, or do they have an agenda they wish to see fulfilled? Or is it some combination of both?
Also, what are they willing to lose to keep their power and to fulfill their goals? These are not the same. For example, a person may be willing to accept another's patronage (losing autonomy) in order to gain more cultural influence (gaining power). And, if goals conflict, which ones take priority?
Next, remember that there is a difference between the organization that consolidates power and the individuals who act upon it. Some people can cultivate power on their own, especially for personal or cultural influence, but often it is the organization that amasses power and the individuals who spend it. Those individuals all have their own agendas or desires for autonomy and so politics is a fractal.
Finally, power does not exist in a vacuum. It is all connected. Every move tugs strings that affect others. There is two major things to consider here--connections among power players and effects of actions.
Some players, in your setting, may be automatically opposed. This is usually because they are drawing on the same source. If the university starts teaching basic physics and machines, the guilds may be upset that the university is intruding on their knowledge-based power.
This immediate opposition has consequences for individuals as, in order to keep drawing on their institution's power, they must maintain the rivalry. A new guild master is best friends with a university professor, but they hide this because the guild would revolt if they knew or would expect her to use personal influence on the professor to make the university drop the coursework. Etc.
This conflict between the organization the draws and consolidates the power and the people who use it opens up a lot of opportunities for back-channels and manipulation.
The other type of connection to consider is effects. Every action has an intended primary effect and, often, intended secondary effects. Every action also has unintended secondary effects. Then think through who supports and opposes the primary and secondary effects and why. Also, the same player can oppose one effect while supporting the other. So then you need to think through how they act on that divided support/opposition.
The government passes a law that all laws will now be translated into every language in the empire so that no one may claim ignorance of the law. The intended effect is to stop that line of defense from a group of rebels. The unintended secondary effect is that this grants additional power to the university who house the most translators.
The rebels oppose the law because it limits them by reasserting the empire's control over them. The church also opposes the law because they do not want the university to grow in power. However, the church does support limiting the rebels. So, the church makes a show of supporting the law in public, but then works behind the scenes to revise or revoke it in favor of the church's solution to the rebels. Or, maybe, they support the law, but then appoint a few priests to reach out to the rebels in sympathy or take action to require all translators work through the church. Etc.
Anyway. These are just my thoughts on the matter. I hope they're helpful!