Modern democracy
In this article I want to give a brief overview of what I'm going to call "modern" democracy. By "modern democracy", I really mean something like "the Western liberal democratic state", but I've gone with "modern" for a few reasons: the model applies to non-Western states, and the concept of "liberal" is contested between some of the states. What I'm aiming to describe here are some of the main features that people have grown up with in democratic countries, and which tend to be the defining elements of democracy for them today.
States and citizens
One of the most defining features of modern democracy is the relationship between the state and the citizen. The state is the set of political institutions, such as parliament, that have power over a particular area defined by borders. The citizens are the people in that state that are recognised as having an inviolable right to be there and participate in politics. Because the power of the state comes from the power of the people, the state can only exist due to its citizens. But because the state makes the rules about citizenship, citizens can only exist because of the state.
Citizens are the ones who can vote. They are also the ones who have rights. These rights are a list of things that the state cannot do to them. For example, the right to free speech is a rule that the state cannot stop people from saying what they want (though most states have some limits on what people can say). There are also some other rights where the state needs to provide things to people, such as fair trial or security from other states.
Representatives and institutions
The next defining feature is that citizens can stand as candidates and vote for candidates to represent them in democratic assemblies. Once in democratic assemblies, representatives propose, debate and pass laws. There are a lot of different ways that elections can work - for example, the state can be split up into lots of different elections that all happen at once (called districts or electorates or ridings or something similar), or the state can have one big election with lots of winners, where the winners get a proportion of seats that's roughly in line with the proportion of votes they won. And there are all sorts of different styles that fall in between, including some mixing and matching. There are lots of debates about which form of election is most democratic, and what sort of outcomes are best. For example, is it better to have an election that produces a stable government where one party got most of the seats, or is it better to have an election that is more representative of the diversity of the votes, even if it takes longer for the winners to get together and form government and start writing laws?
Assemblies usually have some required procedures to write and pass laws, including a vote of the representatives. Sometimes there is just one assembly (a unicameral system) and sometimes there are two (bicameral), and sometimes there are two but only one really has the power to do anything (I want to call this "sesquicameral"). And people will debate which of these setups is more democratic: one assembly is presumably more efficient, while two adds a layer of scrutiny that can help keep representatives honest.
Most modern democracies have people who write the laws and people who run the departments that carry out the laws. In some cases these are separate (called the "separation of powers"), to try and stop all the power being in one place, while in other places they are the same people doing both jobs (sometimes called "fusion"). Normally judges and the courts are separate from the law-makers, though there are occasions where they are the same, and even when they are not it is often the case that the law-makers appoint the judges.
So the people use their power to vote for representatives who make rules, but they also design institutions that put a limit on how these representatives can make rules because they are a little suspicious of them.
Political parties and competition
Political parties are a common feature in modern democracies. This is when like-minded people get together and organise because working together gives them more power. Parties work together because it is a practical way to raise a lot of funding, to get a message out more loudly, to obtain a lot of seats and form government, and to have voters take them more seriously. Parties tend to propose principles and policies, and many voters find this helpful in making a decision about who to vote for - in fact, many people vote based on party affiliation rather than the candidate themselves.
On this basis, parties tend to compete. One way of looking at modern democratic culture is not that it is about people getting together to work things out as a group, but as a competition between parties and policies. This is the "market model" of democracy, where voters move from party to party based of the party offerings the same way customers move from business to business based on product offerings.
Competition is so engrained in modern democracy that campaigns often have debates with declared winners (at least by the media), candidates attack one another rather than present policies, and voter loyalty leads to social division.
Some people think that parties are an excellent way to organise, others think they disrupt genuine conversaton and deliberation between people, some think they connect people to democratic institutions, while others think they make an elite group of politicians. Many people think that parties are inevitable - that people will always want to group together to work together.