Chances are, not very much, but this is dependent on place, area, and the nature of who has taken over.

Let's use the Norman conquest of England as an example. In this case, a relatively small foreign military elite defeated and largely dispossessed the native English elites. The lands of the English aristocracy passed in large part to the Normans. If the land you owned, rented, or farmed in serfdom belonged to a manor that was granted to a Norman petty knight as a knight's fee, you got a new resident aristocrat who spoke a different language than you. If your manor was one of several granted to a more powerful landholder (baron is the general term for a magnate with no overlord save the king), chances are he wouldn't reside there, and your only regular contact would be with a representative of his, who might not reside full-time. In either case, your day-to-day doesn't change much. These manors were largely self-regulating, with appointed officers (bailiff, reeve) from among the peasantry who organized such matters as distribution of land for cultivation (in open field farming, strips of land were assigned from the larger common field, depending on one's property and status, with serfs at the very bottom, free peasants above them, and the lord's set-aside demesne at the top) and grazing. Though, it should be noted that there's some evidence that beginning in the 13th century English aristocrats took a more hands-on management role, but I am not confident enough in that area to go into greater detail. Anyway, you paid your taxes, the lord's representative checked the books occasionally, as it were, and he mostly left you alone.

Where you would be likely to come into contact with an aristocrat was through one of two means. One is through justice. The law courts were dispersed, and the manorial court was presided over by the lord. If you had a dispute with another resident of the manor, you brought it before him and his adjudicated. If you committed an offense against him, he levied fines. He could and did literally act as judge, jury, and (rarely) executioner.

The other way is through military means. During the initial conquest, your land might be sacked and burned as a military tactic, either to impoverish your native lord, or to goad him into battle. This was done by William to parts of the south of England to provoke Harold into the Battle of Hastings. If, after the initial conquest, your region became known as a center of resistance, you might face even harsher measures. The aforementioned William is somewhat infamous for an event known as the Harrying of the North. Northern England was unique in that it had at least partially retained its native nobility, and they continued to bother William, finally rebelling, with Danish support, in an attempt to put Edgar Atheling on the throne. William rode north, bribed the Danes, Edgar fled, and the rebels dispersed to the countryside, unwilling to meet the Normans in open battle. William's response was to ravage the area, burning and looting; if the rebels would not fight him, he would render the economically incapable of fighting him in the future. There is some dispute as to the extent of the devastation, with some authors arguing for a wanton general destruction, and others believing it was more targeted. I tend to side with the latter, as he had a relatively small army and only operated in the region for a few months; but it doubtless left deep scars in the region.