Say I'm a Feudal King, and I'm looking to start a campaign to conquer some neighbouring territory, so I need to build myself an army. I'm wondering what things I'd need to consider to take this process from point A (needing an army) to point B (having an army).
As I understand it, armies were assembling as separate chunks of different lordships and commanders, but were these units assembled from the ground up once the call went out for mobilised troops? Or were there standing units during peacetime that would be called up at that point?
One last thing, I'm wondering how accurately portrayed the assembly of units in games like Total War are, whether you could go down to the local bowers and request a unit of archers, or whether military units formed naturally only after which would any consideration for coordination take place?
There are some really good books that go in to this, mostly from the English perspective, though. Particularly regarding the Agincourt campaign. Check out Ann Curry's Agincourt: A New History for an accessible layman's reading.
To answer your questions, the Total War games gets it totally wrong on several levels. There were no "standing units" (with some minor exceptions), and units were rarely homogenized (with the possible exception of heavy cavalry, but even then it would be a mix of knights and other men-at-arms). Crusader Kings 2 gets this a bit closer. The Total War games are games first and accurate historical recreations somewhere around 125th.
From my looking in to the Crecy and Agincourt campaigns, it appears as if the King would announce his intent to go on campaign and put out word to his lords to gather their men (each lord was responsible to bring a certain number of men, depending on his station) and meet at a predetermined point at an agreed time (e.g., the port at Portsmouth, in the first week of July). In the buildup to Crecy, the sheriffs were tasked with recruiting a quota of archers in their shires. These men were volunteers who signed on for a set wage. Though several nobles and their retinues answered the call to arms, by this time the English were relying heavily on "scutage", or a form of tax paid by the lords in lieu of military service with the express intent of hiring mercenaries (which the yeoman longbowmen hired by the sheriffs were).
Even centuries earlier than the Battle of Crecy, in the days of the Anglo-Saxon Fyrd system of raising the army, the army was by no means a standing one. Local freemen would be required by law to own arms and armor according to their social rank and to report to a predetermined location at a preset time when called up. They then served a set number of days, and then returned home. So, the army (though really more of a militia) might be called up to raid a neighboring kingdom or to defend against a marauding band of vikings, but they were not by any means a standing force.
I would recommend you read "War in the Middle Ages" by P. Contamine, probably the most comprehensive work answering all your questions. Be prepared for some surprises.