Organisation of mercenaries

Mercenaries were usually bought by unit, from their sovereign or other commander, so that they would fight as a unit. It was generally too hard to recruit individual mercenaries one by one and make them all fight the same way. The commander or ruler was responsible for paying his men from the proceeds of the "sale," but mostly paid them as little as possible, and pocketed the difference.

Officers of the hiring army would be most likely check out a mercenary unit if this was a one-time transaction. If the hiring army had bought "regiments" from the same king before, they usually knew what they were getting.

Some details of which kings sold which troops to which people During the war of the Roses are here.

Another example of this was the Hessian mercenaries hired by the British during the Revolutionary War.

As a start on a more comprehensive answer to this question, let's begin with some good source material available online.

This paper from the United States Naval Academy looks at the distinction between "hired soldiers" and "soldiers for hire" in the period 400 to roughly 1066 AD in Britain. It covers, amongst other issues, (some of) the origins of our instinctual disregard for mercenaries in the relationship between Celtic and Anglo-Saxon employers of mercenaries, and the mercenary soldiers employed by them prior to the Norman conquest.

Military Organization of Society, at least in the 80 or so pages available for free preview, looks more generally at the parallel development of our modern society and the modern army, in Europe from about 1000 AD to the present.

Finally, this online article looks in some detail, slightly romanticized, at key concepts in Medieval Warfare including the recruiting, pay, and organization of both mercenary and other troops.

Dozens of books, articles and offprints can be found on the famous Italian Condottierri in even the most cursory Google search. Best known for the staged bloodless battles of their later days, they originated as true mercenaries rather than fantastic stage troupes (sic).

As this article above notes in the section on Pay For The Troops:

Going into the 14th century ... [pay scales table elided]. This comes to about 2,000 ducats per man on average [for 90 days service], although in practice the employers could get off with paying about half that by passing out IOUs that were never honored. This was a game in itself, and was one of the reasons kings, and other magnates who hired troops regularly, surrounded themselves with loyal, well paid and permanently employed bodyguards. There were threats and assassination attempts by unpaid soldiers, especially higher ranking ones owned (sic) hundreds of thousands of ducats.

and in the sec following section on Pillage, Plunder and Ransom: (my emphasis)

Even if the agreed upon pay were not forthcoming on a regular basis, the troops could be kept loyal with sufficient opportunities to pillage the countryside and plunder particularly rich places (like towns.) There was a lottery aspect to this, because rich opportunities did not always present themselves during a campaign. But a share of the plunder could make even a common soldier rich beyond his fondest dreams. Even without hitting the jackpot, just traveling around with a large bunch of armed men presented new opportunities to enrich oneself. In most Medieval armies, it was expected that the troops would "live off the land." Living off the land did not mean that they would go hunting and live off nuts and berries from the forest. A more accurate term would be "live off any unarmed locals." It meant that any food or other valuables encountered as the troops moved along was free for the taking. The nobles leading the army would discourage the troops from pillaging while in friendly territory, which was why everyone was eager to "take the war to the enemy." Once on the lands of the enemy, pillage was encouraged. This not only demoralized the enemies population, but it made your troops happy and gave you the opportunity to skip a pay day and get away with it.

From the above, and reading between the lines, it is soon obvious why French kings were so eager to supply mercenaries to various English factions during the *Wars of the Roses. It immediately resulted in various trouble-making bodies relocating offshore, who when dismissed half-paid would then pillage the English countryside until apprehended or re-hired elsewhere.

In that circumstance, if I were the French king I think I would lend money to various English factions to get them started on transporting my unwanted mercenaries to England. Oh! Wait! Isn't that exactly what various French kings actually did?