Surplus-value and exploitation took a specific form in a capitalist society, but had existed long before Capitalism. Marx claimed that all history should be thought of as the history of class-struggles over surplus-value. That is, the theory of surplus-value is a theory of history:
No classes or surplus-value existed in prehistoric times, however.
Early societies were undeveloped, and as a result their labor-productivity was so low that they could produce only enough to assure the reproduction of the tribe or band. In these circumstances they practiced "primitive communism." This was necessary for survival: if each person did not produce according to her or his ability, and share with others according to their need, the group would not survive as a group, and no individual could survive for long without the group. Thus there could be no exploitation, and these early societies (Marx guessed) would be equalitarian and free, albeit very poor. There is a good deal of anthropological evidence consistent with Marx' guess on this point.
It does not mean that these "primitive" people are nice -- some could be very violent to outsiders -- and when in fact there is not enough for the group to survive (often because the people have been deprived of their land by more developed outsiders), the individuals who are strong enough may turn on the weaker ones in vicious competition for food. But there is no stable exploitation in these primitive societies, and left to themselves they tend to be equalitarian.
The earliest historic stages of society Marx spoke of as "slave" societies. Marx was thinking of classical Greek and Roman society, in which slavery played a relatively large role; but our evidence suggests that the role of simple slavery varied widely among early civilizations.
This has probably caused some confusion. What these societies seem to have in common, and is suggested by slavery, is that exploitation took the form of tribute. The basic unit of society was the city, town or village, and stronger communities extracted surplus from weaker ones by threat. Slavery was just one form that tribute might take, and in many cases slaves were the collective property of the city. Tribute is due from a person as a member of a (defeated) group to another person as a member of a (triumphant) group. Tribute is legitimated theft -- the payer renders tribute in order to avoid violent attack, as the slave works to avoid violent attack by her or his master. This sort of society is hierarchical, in that smaller and weaker towns pay tribute to middling cities that pay, in turn, the larger and stronger cities their tribute. The hierarchy may be reproduced within the city communities, especially the bigger and stronger ones. Emperors and Tyrants rule over mere citizens as great towns rule over villages.
But not always -- our classical examples of democracies are cities in which the citizen-fighters are (in principle) equals among themselves, benefiting from the tribute and labor of noncitizen slaves and villagers.
Because agricultural societies can produce a signifigant surplus over what the farmer must eat to work and survive, tribute and slavery become the basis of life for the non-working class, which includes not only soldiers and rulers but also poets, scholars, scientists, craftsmen, artists. physicians, priests, and philosophers. In brief, the Extortion System was the basis of civilization. But that civilization collapsed and was replaced, in many parts of the world, by a new system called "Feudalism." 
For Marx, the next and intermediate stage was Feudalism, well-known from European history. In theory, exploitation in Feudal society is based on ownership of land. Of course, the landowners have the means of violence, and violence is used to enforce their ownership of land, but it is no longer simply violence to obtain tribute -- rather violence to enforce property in a certain kind of resource. The stage is then set for an exchange: resource for resource, land for labor. But this exchange can never be equal: the serfs have no means of life, in an agrarian society and must offer their labor in exchange for access to land on what terms they can get. Those terms are so poor that landowners become the beneficiaries of "privilege," that is, private law. Landowners are the state; it makes no sense for the state to pay taxes to itself; therefore landowners pay no taxes. And workers may be deprived of the freedom to move, "bound to the land," and even bought and sold little differently than slaves. At the same time, Feudalism is more individualistic than the tribute ("slave") society. Tribute may still be paid by a village community, but it is paid to an individual landlord; and increasingly it is a matter of the exchange of labor service for access to land on an individual basis. This individualism in the ruling landowner class correlates with the highly fragmented nature of Feudal society; but it also leads to the first real conception of freedom. The landlord is (ideally) free, a sovereign individual whose relation to others in his class is essentially reciprocal. And this is the concept of freedom that moves modern society. Rightly, it is the Magna Carta -- the charter of liberties of the great landlords of feudal England -- that people in the English tradition see as the foundation of their freedom.
Feudalism is a class system. There is a class of land-lords, and a class of landless farmers. The land-lords do not work at farming. They are fighters, and in theory, it is their job to protect the farmers from any attempt at extortion or enslavement by other fighters. But the result of this class division is that a class with land, but no supply of labor to work it, faces a class with labor-power but no land. The compromise between the two classes is that the farmers spend part of their time working on the land-lord's land, and in return the village gets access to a supply of land they may work for their own food. In addition to this exchange of land for labor, the land-lord "protects" the village and the village supports the land-lord's fighting with loyal service, which may include some fighting. (In other words, the local land-lord is the ruler of the village). Thus, land is not simply the land-lord's property. The village has rights in it, and individual villagers have rights in it as members of the village community. Conversely, the land-lord has rights in the labor of the village, and the villager may not be allowed to leave the village community without the land-lord's permission. He is then a "serf," and in extreme cases such as that of Russia, the serf's status may be only slightly better than that of a slave. The non-working class of land-lords were known as the nobility, or, in a term from Greek societies, aristocracy.
These complex, reciprocal rights are hereditary and are guarded by custom and tradition. This is a "traditional" economic system in that sense. As a result, it is not very flexible. This powerful role of tradition, together with the difficulty of concentrating local resources to support "civilization" as the older societies did, lead us to think of the feudal society as a "dark age" of ignorance and backwardness. Yet, when they were not under the stress of invasion or epidemic, feudal societies could be very progressive. In Europe, the introduction of wind and water power, and a resulting "industrial revolution," coexisted with feudalism.
All the same, some kinds of production could be better carried on in cities. As feudal societies evolved, cities became important as centers of trade. But these cities could also be productive in craft manufacture, and the combination of trade and craft manufacture made them powerful. A village might become a city, organize a city defensive force and throw off the land-lord who had formerly been its "protector," buy its food for money in the countryside, build a wall, and become a sovereign city. (In some cases the wealthy city simply bought its feedom from the land-lord).
This meant that the two old classes, land-lords and farmers, now faced a new "middle" class that relied much more on money and markets. The city, with a wall, became a "burg," or bourg, and so the new class were called (in Marxist thinking) bourgeoise, burgers.
The cities were the beginning of capitalism, but at the beginning they were more feudal, in their way, than capitalist. To be a citizen was to own a kind of right, like but not quite like a property right. The citizen's right included freedom from the traditional obligations of the serf. Thus, to be granted "the freedom of the city" was to be given a right that may have cost a great deal in real resources to secure, by purchase or war. While food had to be gotten from the countryside, by trade, the apprentice and the servant probably were not paid in wages, but given food from the master's kitchen, clothing and a place to sleep. The market hardly touched them, directly. The city's defense force was not paid, but was a body of citizen part-timers, responding to the city's call to war much as the village serfs might be required to respond to the land-lord's call to support him in war.
But these things gradually changed. With the growing importance of the cities, the money economy grew in importance, and land-lords increasingly released the villagers from the obligation to work on the land-lord's plots, accepting a money rent for the land used by the individual villager instead. Money could be used to hire mercenary soldiers. In some districts, such as the forest cantons of Switzerland, villagers imitated the cities' methods of organization, forming their own defense forces and throwing off their land-lords. Some town and district defense forces were so successful that they hired themselves out as mercenaries -- even today, the Swiss Guard in the Vatican remains as a relic of that transition. Mercenary armies, paid by rich cities, might defeat the assembly of feudal land-lords and part time village fighters and the city thus replace the feudal land-lords as the rulers of the villages. This seemed a re-birth of the ancient societies that had been built on tribute; but it was quite different. Most importantly, taxes paid by individuals replaced tribute paid by village communities, and the cohesive and effectively sovereign village was less and less a factor.
Capitalism was emerging, but it required two things. One was the emergence of national states. The national state is, essentially, a feudal city extended to the territory of the nation, with its own paid army of mercenaries or (professional) national forces, and taxation on individuals to pay for this army. In England, in the English revolution, a paid national army of the English Republic met the aristocratic army of English feudalism and beat it. When the English monarchy was restored, it simply adopted the army of the republic, red coats and all. In France, the national army was created by the king. Either way, the existence of a national army meant the divorce of the land-lord class from its special function as fighters. The second step was to eliminate the special rights of the land-lords and the village community in land. In France, that took place in the revolution of 1789, when the villagers simply took the land as individual property.
In England, the land-lord class were transformed into a class of capitalist landowners who rented their land for money. We can now call them landlords, rather than land-lords, because now they are no longer rulers -- lords -- by virtue of owning land.
Thus Feudalism gave way to capitalism. Still, the hand of violence is concealed behind (and restrained by) a system of property. But property is abstracted. It is property in general -- not in a specific resource, such as land -- that is enforce by governmental violence, and forms the basis for exploitation. Conversely, the connection between the exploiter and the worker is no longer an exchange of resource for resource, but an exchange of resource (labor) for money. The worker's access to productive resources has been entirely alienated. The worker has no access to resources she or he may use for production for her or his own use, but must submit to the regimented direction of the employer. But, at the same time, the working class is stripped of all the special identities that had formerly marked the worker for exploitation. She or he is exploited not as a resident of a particular village or town, or as a slave of a particular master, or follower of a particular lord, but simply as a worker. Thus the working class as such emerges, and this new class has the potential to create a new, post-historical society without exploitation. The exploiting class requires the working class, but the working class does not require exploiters, and eventually will dispense with them, organizing production for its own benefit as a class. This new society is "socialism." Capitalism replaced feudalism through a series of revolutions, in which the class of "capitalists" or "merchants" fought and defeated the class of landlords. The emergence of the new socialist society will be no less revolutionary, in all probability. But these new revolutions will mark the end of the historic tale of classes, exploitation and surplus-value, and a return to the equality of prehistoric societies -- but without the poverty they had to endure.
That's a summary of the Marxist theory of history. It is hard to evaluate such a theory as simply "true" or "false." Unavoidably, there is much in a theory of history that rests on interpretation and even conjecture. But what are the alternatives? Most theories of history are based on some belief in the supernatural. Marxism is not: it has attempted to account for the great trends of history on the basis of human mind and material nature. Perhaps the reader will be able to name a theory of history that has done this more successfully. I cannot.