This is something that we've got very little evidence for. I'm less aware of continental evidence so I'll stick to England and Wales in the 15th century if that's all right, given that that seems to be the period you're referring to. Documents related to indentures and musters tell us how soldiers were equipped, but not how they fought. Chronicles from the period can give us a good idea of strategy but are less useful when it comes to tactics. They do nonetheless differentiate between cavalry, infantry and archers. The latter would make up the bulk of a typical army, though of course they would carry effective melee weapons as well, and wear some armour. Edward Hall's later chronicle describes how the Lancastrian archers fell back after losing the archery duel at the Battle of Towton, implying that more heavily armoured men would lead the infantry assault. This of course, make perfect sense, as those men would be best protected against the enemy's arrows.

This does not mean, however, that there were dedicated 'units' of knights in full plate armour. A line in the Historie of the Arrivall of Edward IV in England and the Finall Recouerye of His Kingdomes from Henry VI seems to indicate the opposite:

of horsemen, he chose, out of his fellashyppe, ij speres, and set them in a plomp, togethars, nere a qwartar of a myle from the fielde

A 'spear' or 'lance' was a term for a mounted man-at-arms. The wording very much indicates that Edward had to put together this force, that there were no pre-existing large units of knights. This makes perfect sense given that knights traveled to battle with their own men, and presumably would have much preferred to fight alongside their own retainers than strangers. We can therefore imagine knights fighting not in separate units, but alongside less well-equipped men from their own locality. It would make little sense to leave the poorest and least-motivated soldiers without their local leaders.

As for how knights actually fought on foot, there are fight manuals that tell us how the poleaxe and longsword were used. These do not, however, tell us much about how knights fought in relation to their comrades. Experimentation though can improve our understanding. A knight in full plate armour is near-invulnerable, but does have weaknesses. If a knight was surrounded he could easily be wrestled to the ground and stabbed through a gap in his armour. As such it is theorised that soldiers may have fought in pairs, with one protecting the other's back. Another major consideration is that fighting in full plate armour is incredibly tiring, especially because the visor restricts breathing. Experimentation has shown that knights could only have fought for a few minutes at a time, in battles that sometimes lasted for hours. They would have needed to have been immediately backed-up by men they trusted, who could allow them to continually take breaks. In Fatal Colours, George Goodwin writes about the likelihood that the best trained and equipped knights would drive at the enemy, laying into them with their poleaxes while the slightly less well-equipped men-at-arms would support them.

In England, pikes tended only to appear in the hands of continental mercenaries. The polearms used by the less wealthy infantry (bills, glaives, halberds, spears) were generally a similar length to the poleaxe (about 6 ft). So actually the equipment of the other infantry had the same tactical use as that of the knights; it was just of lesser quality.

/u/RhegedHerdwick has provided some background on how the War of the Roses was fought, so I'll focus on how the Hundred Year's War was fought.

First, some background.

High Medieval tactics largely revolved around a solid body of infantry in the center of the field, usually with archers and crossbowmen out in front, and knights placed either on the wings of the army or, more usually, in front of the infantry forces. There were many, many variations of this arrangement, and in particular we see Anglo-Norman knights dismounting to fight at the front of their army and keeping only a small mounted reserve, but by and large it was the clash of cavalry rather than the clash of infantry or the clash of cavalry on infantry that won or lost the battle. With their commander dead, captured or fled, infantry formations rarely stayed and fought to the death.

This is not to say that medieval infantry weren't effective. The popular view of medieval infantry as poorly armed serfs is very much due to early modern and Victorian scholarship, and hasn't held up to modern scrutiny. When sources are examined critically, sources rarely reveal an instance where cavalry actively defeated infantry and several notable instances of infantry resisting cavalry quite strongly (eg: the battles of Northallerton Legnano). The reason for the defeat of the infantry was the loss of their cavalry, because without it they were vulnerable to flanking attacks and being cut off from their line of retreat. The loss of their commander was also very demoralising and another major factor that caused them to break and run.

What changed in the 14th century was the development of much more tactically aggressive, well armed infantry in areas such as Flanders and Scotland and the English and French reaction to these changes. The Scottish, for instance, developed from the static schiltron of William Wallace that was shot to pieces at Falkirk to the aggressive schiltrons of Robert the Bruce that charged the English at Bannockburn. In Flanders, more frequent revolts by the towns against their count and the king of France resulted in armies that were mostly infantry and which made up for their lack by using man-made or natural barriers and aggressively advancing when the French were disrupted by these or, as at Mons-en-Pévèle, the French had given up the attack and retired for the day.

I'm simplifying a lot here. Bannockburn was won as much by the mistakes Edward II made as by Robert the Bruce's excellent generalship in exploiting them (especially in neutralising the archers), while the Flemish aggressiveness didn't always stand them in good stead, as at Cassel when they found their surprise attack to be anticipated and were attacked from the flanks and rear by French.

The big difference, and the main factor in how most of the HYW was fought, was the English and French responses to their defeats. The English system of warfare, essentially the same as the French, could still have won at Bannockburn if the archers had been properly supported and the infantry had been placed in front, with the cavalry waiting on the flanks to charge in when the schiltrons had become disordered. No tactical change was really needed, but a tactical change developed over the next two decades nonetheless.

Quite possibly as early as the Battle of Boroughbridge in 1322, we see the English deploying with dismounted men-at-arms in the center of the line and archers on the wings, but the first large scale employment of these tactics was at Dupplin Moor in 1332, where an Anglo-Scottish force numbering around 1500 men defeated a Scottish army several times their size. While not all battles of the HYW would see archers placed on the wings of dismounted men-at-arms, the large scale use of archers supported by men-at-arms would define English tactics for the next 120 years.

In contrast to the English tactical adaptation, the French preferred a strategic adaptations. Namely, under Philip VI the French preferred to hold their position when faced with a stubborn enemy and force them to either take the offensive, surrendering their advantages of terrain or man-made obstacles, or else to withdraw, having achieved none of their aims. While this was a cautious, conservative approach that served him spectacularly at Cassel, it was not very politically flexible. You can only ignore the ravaging of your land and the slaughter of your subjects for so long before you must take the offensive or see a revolt among your nobles.

These two adaptions, one tactical and one strategic, finally met and clashed during the Crecy campaign in 1346. Edward III spent six weeks pillaging French towns and burning the countryside, while facing minimal opposition. Philip VI at first attempted to keep Edward in Normandy, destroying or fortifying the bridges across the Seine and using his army to shadow Edward's. Unfortunately, he underestimated Edward and, probably anticipating an assault on Paris, advanced there, leaving the destroyed bridge at Poissy poorly guarded. As much of the underpinning structure was still intact, the English were able to rebuild the bridge and cross.

Philip withdrew of Amiens, quite probably with the intention of using the Somme as a defensive barrier as he had tried to use the Seine. With the English sacking of Oisemont, and quite probably under a lot of pressure from his nobility, Philip took up the offensive and, crossing back to the English side of the river, attempted to trap the English against the Somme. He made just one mistake: not realising that, while the ford across the mouth of the Somme (the blanchetaque) was only capable of allowing horses or carts to cross on a narrow front, it was possible for the English archers and spearmen to wade across the estuary at low tide on a broad front and overwhelm the defenders.

Once again Philip pursued and caught Edward at Crecy. This time he had to fight. His political capital was largely expended, and the English had outmaneuvered his attempts at strategic victory. As a result, he couldn't afford to let them slip through his fingers and, pushing forward rapidly in an attempt to catch the English on the march, he not only exhausted his most important troops (the crossbowmen), but forced them to leave most of their defensive equipment in the rear of the army. As such, when he tried to press the attack before nightfall, his crossbowmen were at a major disadvantage.