The classic and most common way for a fantasy country to be ruled, the country is ruled by a King or Queen of a normally hereditary monarchy. If the PCs are meeting the monarch or one of the nobles to ask for help, they will need to know their Court Etiquette:Do's and Don'ts to have any real chance of what they want. The Monarch's power may not be absolute, however-see 7 Ways To Control Monarchs. An unpleasant or greedy monarch can often make harsh laws and his or her kingdom or queendom is a very unpleasant place to be, but with a good monarch everything works well.
Rule of the people, the kind of rule which so many real countries at least claim to have, and which so few countries really have in practise. In theory, the people or at least a large section of them choose what laws to have; in practise this is only possible in small city states, or the cantons of real life Switzerland, as otherwise there are too many people to vote at once. In practise, in most countries the people only vote once every four or five years and the rest of the time, a de facto oligarchy rules the people and claims that it is for their own good. Democracy can become mobocracy, the rule of the mob, meaning in this case the uneducated and volatile people. Perhaps the PCs need to ask a public assembly for help.
The rule of one person who is not a monarch, such a person an easily become an unpleasant tyrant, but that is by no means always the case. Since the ruler was not born to rule, he or she has most likely got good or excellent political skills to gain the prize of rulership in the first place. Perhaps the PCs are trying to either assassinate the autocrat -or to carry out a top secret task for said autocrat in exchange for the autocrat's help. If they fail, the autocrat will have plausible deniability.
Rule of the Judges. In this case, instead of a monarch, a dictator, or a small cabal of people behind the scenes, a public Supreme Court of judges rules the country. At it's best, the judges could be very good and skilled rulers; at it's worse, they could be very unpleasant tyrants, or be too busy to rule the country properly, or just not know how to rule the country. Such a country will be even more law bound then most, and lawbreakers will not be treated well. The Islamic Courts were a short lived real example of this kind of government. Perhaps the PCs are on trial for their lives, in which case having a group of 30 Lawyers to choose from would be very handy.
A small group of people either openly or behind the scenes (or a mixture of both) rule the state. The argument is that a monarchy or an autocrat would be a tyranny waiting to happen, a theocracy goes against freedom of religion and would be awful, the judges were never meant to rule, and the people are too stupid to be allowed to rule. The most common de facto method of rule in real life.
Rule of the Priests. A single religion rules this country and the chief priests are the rulers, and the practise of other religions or atheism is simply Not Tolerated, with at least a possible death penalty for those caught not following the national religion, even if executions are rare in practise. Iran is a real life example of this method of rule, with the Vatican City as a kinder, smaller and gentler example of clerical rule minus the floggings and executions.
Rule of the S**t. The ruler here only cares about himself or herself. Taxes are far too high, law and order is either non-existent or way too harsh, and things are constantly going wrong. Somalia, Afghanistan, and some would argue, the rule of Donald Trump are examples of this unpleasant kind of rule. In a fantasy world, cities ruled openly by Thieves' Guilds could also count as examples. No ruler or group of rulers will ever openly admit to being a Kakistocracy of course, as that would be inviting an open rebellion to break out, and most rulers think they are ruling well anyway. PCs look to your swords and be careful when passing through this country.