Becoming king
Becoming King in the SCA
The usual way to become king in the SCA is to win a crown tournament. A less common way to become king is to be the consort of a fighter who wins crown tournament. As a method for choosing a king, it has a number of advantages. The main one is that in order to be good enough to win a crown tournament, it is likely that the victor will have been involved in the SCA for a respectable amount of time.
There are a few drawbacks with this, not the least being that certain SCA demographics are over-represented. This is probably not as much of a problem as some may think, as the first three reigns of the Kingdom of Lochac say three Laurels take the throne (two Queens and a King).
Historical methods of becoming King
Surprisingly, one of the arguments that is sometimes promulgated for the crown tournament model of selecting Kings and Queens is that becoming King by right of arms is period. Certainly, it is true that many Kings were crowned after having conquered a Kingdom, but none became King by winning a tourney. Here are some examples of how Kings were really chosen.
Inheritance
The most common method of becoming King was to inherit it. If you were the eldest son, you would become King upon your father's death. It took a while for this to be formalised in a number of countries (William Rufus was not the eldest son of William the Conqueror), but it did make things easier. There was less likelihood of trouble if everyone knew who was next, even if it was an incompetent twerp.
Election
You may be familiar with the Monty Python quote You don't vote for Kings. It's not quite true. It is true that there was never a Presidential style election for a King. That would mean peasants got to vote, and in spite of the best work of the levellers the vast majority of the nobility would never have that. Usually it was a group of interested parties involved, as in the witan. For "interested", read "self-interested land holders who could raise a large enough fighting force to cause trouble if they didn't get their way". As well as the Anglo-Saxon Kings of England, Hugh Capet was elected as King of France.
A King can make a King
We know next to nothing about Hugh Capet, which is a shame because he seems to be a very clever guy. He started a dynasty that lasted centuries without anybody noticing. Nobody thought that there would be a Capetian line of Kings except Hugh, who raised his son to the throne before his death. The two ruled in tandom. Hugh died, his son ruled alone. That is until he raised his own son as co-King. Several generations later nobody questioned that the French crown was hereditary.
Conquest
William the Conqueror pulled off this trick at the Battle of Hastings.
Notes by Anton about historical Kingship
Although you couldnt generally become King by an election, the only way to become Holy Roman Emperor - who out-ranked any King in Christendom - was by Election by the Imperial Electors. A copy of the Golden Bull of 1356, that defines and regulates the election, is here ... http://www.yale.edu/lawweb/avalon/medieval/golden.htm
The important city-state of Venice also had an elective Doge, or Duke.
Another important medieval idea is what a King is ; a King is a Prince who is Soverign in his own domain, who has either personally or by his predecessor, been invested in the title of King by the Pope.
To be Soverign means that a State does not have to answer to another worldly power for it's acts ; the city of Florence is soverign, while the city of London is dependant on the King of England and thereby not. If a city or a states does not make lawful war without reference to another, then it is almost certainly not soverign.
Note that some Princes who are not titled Kings, such as the Counts of Savoy, are soverign, as in no other Prince can lawfully command them ; but although they are Emperors in their own domain, they do not have the title of Kings.
The Lord of Milan, Gian Galeazzo Viscounti bought (as in, for cash) the title of Duke of Milan from Emperor Wenceslas in 1395 ; he attempted to be invested with the title of King, but this was not granted by the Pope.