Designing an entire country can be a daunting task. Remember that you only need to include elements relevant to your world. If sewer systems are not your thing, don’t spend time creating them. If that’s where the mutants live though, they might be worth thinking about.
It may be useful to first think of a name for your country. Consider its language and what the people would refer to themselves as. Countries may have both common use names and official names.
Territory & Borders
It may next be useful to place this country within the context of the broader world. Creating a map that outlines the territory of this land may be useful. Borders often fall along natural terrain that is either easy to identify or hard to cross/easy to defend. This includes rivers, mountain ranges, seas, lakes, and deserts. These borders may have changed over time, so consider the history of these changes and what happens to the people left behind as the border moves. It may also be worth considering the landscape of the country itself: is it predominantly forestland, desert, a frozen wasteland?
What does a border crossing look like in your world?
Cities and Towns
Countries will contain population centers as well as sources of food for its people. Consider where these are located as well as their general characteristics.
Roads, sewage systems, energy production sites, etc are all examples of infrastructure. This may not be detailed to any extraordinary degree depending on how you plan on using your fictional world, but it’s at least worth considering how the general people move throughout the area and what exists to make their current lives possible (or how it has all fallen apart if your world is one trending towards the apocalypse). If your world is of a more fantastic sort, consider what makes it fantastic and how infrastructural elements fit into this. For example, if the country is subterranean, are there support pillars? If the country is aquatic or cloud-based, are there mooring balloons to keep it stable? If your people use teleporters to move around, are there main hubs to do this?
Countries may be organized in different manners, from republics to monarchies. Countries that are near or adjacent to one another will often have the same or very similar styles of governing themselves.
Hell is a constitutional demoncracy. Heaven is for anarchrists.
Flags & Banners
Most countries will have a flag, banner, or other visual element that helps identify themselves. These flags will be specific to the country and highly symbolic of that country’s values or history.
Leaders may be political, religious, economic, scientific, military, or other in focus. They may be popular, or extremely disliked. Some may be figureheads, while others may wield absolute power. A leader may make singular decisions or may act in counsel with others. Consider who your leaders are, and how they perform this role.
Countries usually do not exist in a vacuum. They will have trade partners, allies, enemies, and external threats. Perhaps these outside elements are other countries, or perhaps they are something else entirely.
Wherever there is power, there are plots to claim it. Countries may be calm and peaceful or may be amid massive internal strife. Coup attempts may be underway, riots may be taking place in the streets, or important laws may be being made.
Remember, internal politics can be coopted by external forces. Who is really behind the push for independence?
Determining the economic forces of a fictional country can be important aspects of worldbuilding. If a country is rich or poor in an important strategic resource, this may drive its’ motivations within the broader world. If the wealth of the nation is highly concentrated, it may mean there is a poor and desperate population ready for revolt. These macroeconomic forces can be used as the basis for important narratives or used to create background tension when worldbuilding.
In game oriented worlds, the economy can be a critical factor in game play. The resources available to each country can be used as trade goods or as a means of production.
Oft Helm’s primary export was iron springs. These were of questionable quality. Oft Helm’s primary import was returned, broken springs.
The history of a country can bind its’ people together, can explain rifts within them, and can help define its place on the world stage. Consider how this country came to be, what it has had to do to survive, how it has changed throughout time (the borders, the people, the laws), and what its’ aspirations are for the future (does it seek conquest or a peaceful existence?)
Law & Order
Different countries will have differing laws. An item or act may be tightly controlled in one territory while uncontrolled in a neighboring one. In addition to having different laws, even countries with similar laws may see different levels of enforcement. One place may have the means to combat criminal organizations while they have become entrenched in another. Differences such as these between places can help add nuance to a world and be exploited for plot in narrative driven worlds.