I am sure you know how this works in most European countries Reg, but for those how don't this is how it works in Denmark (very brief)... : If your party can demonstrate support from a minimum of 2 % of the voters then they can get on the ballot (this is like your primaries - you cant pledge/registrar support for more than one party). The % varies in the different countries, but the principle is more or less the same...

On voting day we then vote for either a person (from a party) or just the party. This typically leads to 6-8 parties getting into our "senate" (there is no Congress). In order to form a government one of the two biggest parties usually makes deals with enough of the rest to get a majority and they then build a government with those parties or they build a minority government alone (with the assumption that they wont get overthrown by the supporting parties - this might not work out after a few years ;-) which will lead to a new election... ).

Since we are still a monarchy, the queen is sort of head of state, but she has no real power whatsoever. Power is with the government and the prime minister - leader of the ruling party... however since it almost never happens that a single party has a majority alone, the parties are forced to make compromises all the time...

Notes: An election has to take place at least every four years (varies by country), it typically takes three weeks from when an election is scheduled to the date when it is held, political ads on tv is not allowed, all eligible parties will get 1 one hour on a national broadcaster to present their views (they will get questioned by reporters... ), 2-3 panel debates with the leaders of all parties will be held on a national broadcaster.

Also! most of the government administration does not change when the government changes - they are supposedly neutral (cough) and are supposed to carry out the will of the elected minister in charge. (Meaning that a weak minister will get overruled by the head of the department... ) I think this is a weakness (or strength) in all governments, depending on your POV...