How did slavery function in Early Medieval Society?

How did slavery operate in a legal sense?

There's three cultural areas at stake here: the Roman West, the Roman/Byzantine East, and the (later) Islamic East. In the Roman areas, slavery grew out of Roman legal norms, in which slaves were considered the legal property of another (despite Christianity, which wasn't used to oppose slavery until the 1700s). The Germanic tribes didn't have as stratified of a society, so in those places where Roman slavery survived to any extent, Roman laws must have survived with it. Where society collapsed, as in England and northern France, Roman-style slavery collapsed too, so slavery there probably more closely resembled indentured servitude or household servants.

In the Middle East, Islamic rulers took over a thriving slave system from the Byzantine Empire, so there's lots of early stories about Muhammad dealing with slaves. He came from a small town, though, where slavery was more about social relations than industrial exploitation, so these stories—which formed the basis for later Islamic law—actually have a potential to radically humanize slavery, at least in comparison to the galley slaves and prostitutes of the Roman world.

What was its status?

Chris Wickham argues that the early medieval world was one of regional divergence, so practices of slavery must have diverged as well. Slavery was probably worst in the Eastern Mediterranean, where society was most complex. Here you'd find galley slaves, industrial mines, and prostitution, as well as elites who could act above the law. In areas where society became less materially diversified (i.e. the rich didn't have that much more than the poor), slavery was probably more often regulated by custom and by the opinions of your neighbors. In some places, this might encourage owners to take cruel liberties upon their unprotected slaves. In others, it probably mitigated how harshly they could act.

There's two important complicating factors. First, slaves could sometimes be much more powerful than the average free person, such as an advisor to a caliph or the steward of an estate. Second, because of regional diversity, slaves who traveled could change in status as they went; a slave from Francia might experience many completely different sets of conditions if they accompanied a master to visit Rome, Constantinople, or Jerusalem.

Who was enslaved?

This is a tricky question, and there was an old theory that after Romans stopped winning wars, there was no longer a steady supply of slaves. That's not really accepted as true any more, although the dissolution of the Roman state in the West meant the disappearance of government-subsidized commerce and contracts, which perhaps had previously been met in part through the labor of war captives. There were, of course, wars throughout the early medieval period, so a small supply of captives would constantly have entered the slave market. In many areas, people were probably born into slave status or could be legally reduced to slave status through debt. Some sermons attack parents who would sell their children into slavery or who would abandon their infants to be picked up and raised as slaves. It's hard to know how pervasive this really was, but it happened at least occasionally enough for some churchmen to worry about it.

Were slaves capable of gaining freedom? If so, what was their social status afterwards?

Many slaves in the West probably achieved their freedom as society broke down and there was no longer a pressing need to distinguish slave from free. Roman law did allow for manumission, and usually the manumittor became the freed slave's patron, ensuring that they received some degree of legal protection and social support. A similar process is encoded in Islamic law through the early stories about Muhammad, although Islam uniquely proposed that manumission could merit a heavenly reward. (This can be contrasted to Charlemagne's will, which cashed in some of the treasury as alms for his slaves but didn't free a single person.) Islamic manumission created a large class of people known as mawlas, who have confounded scholars because sometimes they seem like slaves and at other times they seem free. Mawla could probably be loosely translated as 'freeman,' and these individuals probably faced a similar diversity of circumstances to the freedmen of the US South after the Civil War.

What was the role of slavery in early medieval economies?

As mentioned above, Roman slavery had often been for large-scale industrial exploitation. This largely broke down, although some slaves probably continued working in mines and in shipping on a smaller scale. Most slaves probably either worked in households or engaged in farming or animal husbandry. For example, Saint Patrick famously spent three years herding cattle as a slave in Ireland. There were of course larger projects, like Charlemagne's efforts to dig a canal between the Rhine and the Danube, or massive irrigation work in Syria or the construction of Samarra in Iraq. These projects likely depended on slave labor, at least in part. Women seem to have been particularly valuable as slaves, perhaps because of their gendered abilities to make textiles and nurse children, which were vital household tasks in the early middle ages. Women (and also men) might have been sexually exploited as well. One of the more creepy aspects of medieval slavery is the prevalance of young male children, who could be molded into whatever their buyers wanted. Venice in particular seems to have provided a steady stream of eunuchs drawn from the wars of Charlemagne and his successors.

How did contemporary philosophy and theology make sense of slavery?

To put it frankly, slavery was considered a part of society, and neither philosophers nor theologians really thought of a world without it. If they did, the New Testament could be searched for precedents allowing slavery, whereas the Old Testament was used to justify new forms of indentured service to the church, i.e. the practice of oblation where parents would gift their children to the church as monks or nuns. Jennifer Glancy's Slavery in Early Christianity (2002) is a stunning read, and Mayke de Jong's In Samuel's Image (1996) gives a thorough survey of oblation. Unfortunately, the most thorough works on Islamic slavery are either revisionist or downright Orientalist and can't be trusted. Perhaps the best read is a short article by Matthew Gordon, "Preliminary Remarks on Slaves and Slave Labor in the Third/Ninth Century ʿAbbāsid Empire," in Slaves and Households in the Near East (2011).

Let me know if I misinterpreted any of your questions, or if you want any further details. That was pretty quick and dirty, and there's lots of great information out there.