On September 9, in the year 1087, William the Bastard, known for twenty-one years as the Conqueror, was at Rouen after falling ill during a siege at Mantes. Orderic Vitalis writes:
At length, on Tuesday, the fifth of the ides of September, the king waking just when the sun was beginning to shed his rays on the earth, heard the sound of the great bell of the cathedral of Rouen. On his inquiring what it meant, his attendants replied: "My Lord, the bell is tolling for primes in the church of St. Mary." Then the king, raising his eyes to heaven with deep devotion, and lifting up his hands said: "I commend myself to Mary, the holy mother of God, my heavenly mistress, that by her blessed intercession I may be reconciled to her well-beloved Son, our Lord Jesus Christ." Having said this he instantly expired.
The physicians and others who were present, who had watched the king all knight while he slept, his repose neither broken by cries or groans, seeing him now expire so suddenly and unexpectedly, where much astonished, and became as men who had lost their wits. Notwithstanding, the wealthiest of them mounted their horses and departed in haste to secure their property. The inferior attendants, observing that their masters had disappeared, laid hands on the arms, the plate, the robes, the linen, and all the royal furniture, and leaving the corpse almost naked on the floor of the house, hastened away.Medieval politics are endlessly interesting. We've seen an aping of that in the extremely popular Song of Ice and Fire series (even if they're simplified and not truly medieval). What about medieval politics draws people, particularly those interested in fantasy, to them over and over again? It may have its origins in the intensely personal character of the medieval polity.
The state was often held together by bonds of personal loyalty. Part of understanding medieval politics is understanding the relationships of its players. Family was important, obviously, since brothers and sisters could be used to form powerful alliances with the church, with other families, etc. The same goes for children.
How can this be used in fantasy writing or gameplay? The first and foremost thing I would recommend is the creation of the actual characters who play a major part in any politics. Understanding their individual motivations, much more so than early pre-modern or modern politics, will make the objectives of their "factions" much clearer.
Indeed, drawing a flow-chart like document that shows the relationships of the major figures to each other can assist in understanding why certain people behave in certain ways in the interior of a kingdom. The corollary to that, of course, is to understanding the intrafamilial dynamic of each major noble house. It may very well be possible for a trio of brothers to despise one another, and for that to cause major political turmoil and upset (for example, William Rufus, Henry, and their older and nicer brother Robert).
Treating a political melange as a whole system heuristic will give you a much firmer understanding of how any one shift may affect the network. I've found this useful when mapping out the complicated routes of elvish politics in the 10th Age. Of course, this all depends on your players. Some folks don't want complex politics interfering with their gaming. I think it adds an interesting shade of realism to know that whenever a PC completes an adventure someone is benefitting from it somehow. And when you know how that person is benefitting, you can better see how the PC's actions affect the dynamic world.
In some ways, this is a plea to make fantasy worlds as interesting, complicated, and realistic as The Wire.