Here’s the situation in Norway:
Head of State is King Harald V. The best way to describe his situation is that although he can at times wield considerable political influence, he has no real political power. Norway is incidentally one of the few countries to have voted to become a monarchy, after declaring the union with Sweden dissolved in 1905.
The real politicial power sits with Parliament (Stortinget). Members of parliament are elected every four years. Each of Norway’s 18 counties, plus the capital of Oslo as its own voting district, is assigned a number of representatives which is supposed to be in proportion to its population, though in practice the low-population counties are overrepresented. The representatives for each county are divided according to the percentage of votes cast for each political party. There are also a number of equalization mandates which are distributed at-large according to a hideous set of mathematical equations, so that parties who got a small but significant number of votes don’t get entirely squeezed out.
Voters choose the ballots for the parties they wish to vote for from boxes inside the voting booths. They are allowed to make certain changes to the ballots - for instance, by crossing off names of candidates they don’t want to vote for - or to submit empty envelopes or spoiled ballots which are counted as “blanks”.
Once the mandates are distributed, the usual parliamentary stuff begins - the leaders of the parties try to figure out who can get the most support for their agenda. In theory the King can invite anyone to form a government; in practice it’s understood that he will invite whichever party or coalition of parties has the best chance of forming stable leadership. A government can resign, or be forced out by a no-confidence vote, between elections, but a new government must then be formed based on the current Parliament. Elections are held on fixed dates and Parliament cannot be dissolved.
It’s been a good long while now since any party had an outright majority in Parliament. This means we’ve had coalitions and minority governments. At the moment we have a Conservative (H)-led coalition that includes the Christian Democrats (KrF). Because the leader of KrF, Kjell Magne Bondevik, is much more popular both among his fellow politicians and among the public in general, he was given the post of Prime Minister even though his party is much smaller.
The thing about minority governments and coalitions that are either minority or hold the slimmest of majorities, is that they lead to rather cautious “caretaker governments”. On the bright side, bone-headed political ideas tend to die in committee. Unfortunately, this also means that thorny issues are either ignored or “solved” by watered-down compromises that only serve to delay the inevitable. For instance, at present Norway has become a net importer of electricity, in spite of all the hydroelectric power the country has. Since much of this extra electricity is generated at old, polluting coal plants in Denmark, it is widely seen as a Bad Thing. Several alternatives have been proposed, including a large new natural gas power plant in Norway, wind power, building new dams on smaller rivers, etc. All of these alternatives have their advantages and their drawbacks. Because no political party is strong enough to want to risk making an unpopular decision, the debate goes on, as it has been going on for years, and meanwhile those plants in Denmark keep burning coal for the Norwegian market.
As far as effects on people’s daily lives, it’s really the township and to a lesser extent the county governments that do that. Elections for these governments are held every four years, two years apart from the national elections. These governments get tax money from the state, and a list of duties from Parliament. How they spend that money determines the quality of schools, public transportation, old people’s homes, local roads, etc. etc. The problem is that the money is not always sufficient, and some of the township governments have a real problem with money management. (Trondheim, for instance, has several times funded expensive vanity projects instead of, say, buying new textbooks for the schools.)