Modern armies have clear and concise hierarchies. How would a hierarchy look in a typical western medieval army ? Like the armies that fought in Hastings, Agincourt etc.

So I will focus on Agincourt and the 14th-15th century English armies here as it's more within my speciality and there were an enormous amount of changes. I will also focus on royal armies rather than routiers/free companies (although the distinction can be murky).

In short, they were organized as companies and grouped into larger battalions while on the march and in battle.

A "company" was a group of men, usually from a few dozen to a few hundred -- although greater nobleman would, in turn, lead retinues of close to one thousand. It would be lead by a captain -- usually a member of the landed gentry or nobleman. He would contract a certain number of men to fight under him, usually for the duration of a campaign or a fixed period. They would then contracted smaller numbers of men to fight until we get to the men at arms and archers fighting as individuals.

Companies would often be mixed groups of men at arms and archers, and as the 14th and 15th centuries progressed, archers tended to make up a larger percentage of royal armies (see Jonathan Sumption's Hundred Years War Vol. IV, chapter IX).

English armies often had a greater esprit de corps as the above process (men contracting and subcontracting others into a fighting force under a local nobleman / notable) would often lead to a slice of English country society becoming a fighting force (see Sumption, HYW Vol II, Ch. IV) .

Different battles would have different organizations, but the general English tactic was to group dismounted men at arms in the center with archers on the wings or sometimes interspersed between the men at arms. Each of these units was commnanded by the head of the army or its leading captains. Orders were either given in advance -- especially for the French-- or, as at Poiter in 1356, the English took a more dynamic approach and passed orders around as events evolved.

On march, the armies would generally split into (usually) three separate columns, each lead by one of the main captains, in order to allow for more pillaging allow for these smaller parts of the army to gather their own supplies separately.

For more info besides the Sumption chapters referenced above, I would check out this book on Henry of Lancaster's army. It goes into depth about the contract system and how that specific expedition (Aquitaine in 1345) was organized.