From my understanding, a count was usually vassal to a duke who was vassal to a king and a count had minor manorial lords who were vassal to them. Counties also had baronies inside them and the title of baron was lower ranked than a count, but a baron was not actually vassal to the count whose county their barony was inside because their land and title cane directly from the king and thus they are only direct vassals to the king. Yet, they are completely surrounded by the count’s lands so how did that work in practice? How would they operate and what were the responsibilities of a baron as compared to a lord of the manor or a count?
I’m sure I got sone stuff wrong and I know the feudal system worked differently in different times and places, but could I get a basic explanation?
The more recent historical perspective is the neat feudal pyramid is a creation of post-feudal lawyers. The actual practice was very messy. In Charlemagne's time a count was an appointed official - usually a notable, but often appointed to an area where he did not have major land-holdings. A duke (dux) was roughly the leader of a subordinate people (so, Bavaria, Aquitaine, Burgundy, Normandy). As Carolingian authority decayed, counts became hereditary and their authority concentrated in their counties. Dukes tended to be nominal titles unless backed by significant power. In the 11th century authority decayed further, to the point that in some areas power lay with local lords (castellans). Then, as central authority revived, power went back up the chain - to the count, duke or king as circumstances dictated. The Counts of Flanders were significant figures, as were the Counts of Anjou, Toulouse or Champagne. Philip Augustus of France asserted that he was direct lord of whoever did not hold of another lord, and used this to exert control over areas where counts had faded out (such as the Auvergne). A lord here would hold directly from the king.
A count could be vassal to another count (as Tours often was to Anjou), a baron could be vassal to someone beyond the county or to a bishop or to the king. In northern Italy, as cities brought their rural surrounds under control, a lord might be vassal to the city. In France or England, towns might be chartered, and so vassals to a count (earl), or direct to the king. In the Empire, the church was a key support to the emperor, so archbishops and bishops are often secular lords as well - plus there were Free Imperial cities, towns, villages and knights (holding direct allegiance to the emperor).
So, in practice, while a baron might show courtly deference to a count, their relationship would be more governed by who had the most land and influence. Someone like the Sieur de Coucy was proudly independent. Moreover, fidelity (taking an oath not to injure someone, and to offer support and counsel) usually implied subordination, it was often separate from a benefice (a grant of land or other reward). A count could build up a network of fideles or enforce his right of justice without necessarily gaining any rights over their land. In England after the Conquest the two went together, but often not before 1200 in France, and the Empire was different again.
Further reading:
Susan Reynolds: Kingdoms and Communities in Western Europe 900-1300 and Fiefs and Vassals
Jean Dunbabin: France in the Making 843-1180
Peter Wilson: Heart of Europe (on the Holy Roman Empire)