Politics are a complicated enough subject when you're not making them up whole cloth. There are so many variables and so many different points of view to consider. A single political entity may contain not just the members of the governing body of a given nation, but also anyone who has the power to influence them, such as religious leaders, the leaders of social groups, powerful guilds or unions, and wealthy merchants. Within that political entity everyone has their own agendas, concerns, goals and views and they are all trying to move them forward. Some will work together, some will not, both for a variety of reasons which range from personal dislike or rivalry to disparate worldviews or agendas.
But they all need one another. In most political systems it's not easy for one person, even one powerful person, to get something done. Support may be required in the form of votes, or public support, or money. There's always give and take in the political structure and as complicated as that makes things, it can also produce tension and conflict, become a way to bring together characters who would normally have nothing to do with one another, or influence your plot.
This is just as true for nations as for individuals. A nation which exists in a vacuum can do whatever it wants, but one that has to deal with other nations also depends on those nations. Whether it's for resources, goodwill, or backup in a fight: nations interact. I find it helpful to think of nations as “meta-characters.” While their opinions, desires and needs are made up of thousands of different parts, they still have these things. Thinking of them this way can help you determine how different nations interact and how they are likely to respond to one another throughout the course of the story.
When building the politics of my worlds, I like to start at the top. Create the basic ideas of the different nations, figure how what they have and what they need and where they can get it. I consider them as characters, each with their strengths, weaknesses, and agendas. Their beliefs play a role in this—and any internal conflict of belief should as well—but they also have real, physical needs. Perhaps they’re a desert nation and wood must be imported, or they’ve got no access to water-based trade routes and need to move their goods through a neighboring country. Perhaps they’ve been fighting with another nation for centuries and they’re worn out and need back up.
These are just as important to a nation as food and water is to a character. These are the things which drive them and enable them to be a nation. Without resources, they fall apart. So who can they go to in order to get these resources? What does that nation want in return? Are they happy with the price they have to pay to get what they need?
Once I’ve got the big picture planned out, I generally move inward. The next step is the politicians themselves (and anyone else who has that kind of power), who will all have different views and motives. They’ll all want different things for their nation and have different views on how best to get those things. How in-depth you have to go with them depends on how big a part they play in your story, and how likely they are to have conflict with the main characters. Knowing, in general, how the big political players feel and what they want can show you where your characters are likely to run into problems as well as allies.
Then I like to consider how all of this affects the main characters. Whether you’re writing political fantasy or not, the characters are going to have opinions on their nations. Its policies and resources have repercussions in their lives. Perhaps the ban on importing certain goods makes it impossible for them to get materials for their business, or an alliance with a neighboring nations means that their business is booming because it opens up a new market. The nation’s views on the character’s religion, ethnicity, social class, magic, sexual orientation, gender, occupation, etc. all have an effect on the characters. And knowing how the nation in general, and the big political entities in specific, feel about those things means knowing your character and the immediate world that they inhabit.