I specialize in the Angevin Empire, so my answer will not be absolutely definitive for all of Western Europe. If anyone specializes in other areas, like the HRE, Iberian Peninsula, Eastern Europe, Crusader States, please feel free to also answer, since I would be curious to see how these compare.

England is an interesting case, as its government was very well-organized, and a lot of records survive regarding the economic and military circumstances of feudal lords in the 12th C. Henry II, who was a master of organization, required tenants-in-chief (meaning lords who answered directly to the King) to report the number of knight's fees they possessing at the death of his grandfather, Henry I, and how many additional knights fees they had created since then. Henry took the throne after a major civil war was fought over the English throne between his mother, Matilda, and his cousin, King Stephen. A lot of the early years of his reign dealt with resolving disputes that had arisen from the two factions distributing the same parcels of land to different people during different phases of the war.

Philippe Contamine sums it up, with some examples, quite nicely in War in the Middle Ages:

They were asked four questions: how many enfeoffed knights had they at the death of Henry I (1135)? How many household knights had been enfeoffed since then? How many knights did their demesne properly owe? And, what were the names of the enfeoffed knights (this last information would allow the king to check those who had not taken the oath of allegiance)? Replies wee contained in the famous Cartae Baronum: 283 tenants-in-chief declared there a total of 6,278 & 7/8 knights' fees, though the servitium debitum [service owed] only amounted to some 5,000 knights - 1,000 supplementary knights furnishing, one might think, a sort of safety net taking into account minors, old men, the infirm and sick. The abbey of Bury St Edmunds, for example, had 50 knights dependent on it althought its servitium debitum was only 40, and the abbey of Abingdon, which owed the king 30 knights, possessed 33 feoda militum.

The knights fees were not necessarily men immediately trained and able to serve at a moments notice, but were units of measurement of income and land ownership. Essentially, it is a measure of a lord's income and wealth, compared with the expenses of equipping and paying knights. This is why the result ends up as a fraction.

If you were a lord serving under a medieval King, you would know exactly what number of men was required of you. It is not very likely that a summons would read "as many men as you can" but would be a more generic summons requiring you to muster the requisite amount of men. The standard, required period of service during Henry II's reign was 40 days, which had been decreased from 60 days at the start of his reign. During Henry II's reign, English Kings no longer required English fiefs to provide men for campaigns in Henry's continental possessions, though many English lords had lands on both sides of the channel, and frequently did participate in conflicts in France.

The King might only summon a part of his forces as well, and in such a summons for service, you would be notified what proportion of men you were expected to provide. He may also summon a specific geographic region, considering that travel may not be feasible or timely enough for his purposes.

Alternatively, if you could not provide the requisite number of men, either because you needed them at home, or did not have enough able-bodied men who could be equipped in time, you could pay scutage instead. In the second half of the 12th Century, the going rate was £ 1 for the 40 day term of service. In Richard I's reign, this was characterized more as a fine that a lord paid to not participate in a campaign. The King could then use this revenue to pay for mercenaries, equipment, supplies, etc. The King might also grant his vassals permission to use scutage among their own underlings, with the caveat that the tenant-in-chief was still required to produce the requisite number of men.

Now, as a mid-level lord, you may owe the King, say 15-20 knights fees. You may have a few underlings of your own who owe you 2-3 knights fees, and several who owe you one, or partial knights fees. Now, you may have some knights beneath you who would be called up from their own estates in order to participate, but as a lord, you probably also have household knights, who exchange protection, company, and prestige for your patronage, and economic security. So you would receive your summons, which would tell you how many men you were expected to provide, and whether or not offering scutage among your own vassals was available, and you would respond according to your preferences, needs, and capability.

As far as peasant participation goes, you see less of it in the 12th century than you do later on, partially because few actual set-piece battles occurred during this period, so peasant participation was not particularly efficient, as they were untrained. However, you might need a large number to accompany your force to act as a support structure (blacksmiths, food preparation, etc.). Most of the actual fighting would have been conducted by the trained and equipped knights.

Sources

Philippe Contamine, War in the Middle Ages

Maurice Keen, Chivalry

Maurice Keen, Medieval Warfare: A History

Matthew Strickland, ed., Anglo-Norman Warfare — An excellent collection of articles. Several involve household knights and military obligations.

Matthew Strickland, * War and Chivalry: The Conduct and Perception of War in England and Normandy, 1066-1217* — This one is definitely one of my favourites and a staple in this topic.