There isn't really a single good answer to this question, as the texture of southern life did vary from state to state and from decade to decade throughout this period.

Nevertheless, one can still make certain generalizations. Free black people in slave states posed a bit of a problem because they occupied a lower position in the racial hierarchy, but did not have the status of legal chattel in the way that enslaved people did. People in this position were frequently the targets of suspicion from local whites, who often saw them as a negative influence on the enslaved. Free people of color did at times enjoy rights to land and other forms of property, including slave property (this usually occurred in cases in which a free person of color purchased a family member in situations that would otherwise require said relation to leave the state). Free people of color could participate in certain trades, but higher status professions such as medicine and law were generally closed to them.

It is also worth noting that the circumstances of someone's freedom could easily affect one's circumstances. Some free people came from families that had free relative going back in the 18th or 17th centuries, though this was not necessarily common. Some people attained their freedom through stipulations in a deceased master's will, though these could be contested in court by creditors or by heirs. Virginia at one point had a law restricting manumissions within certain age ranges. This was meant to prevent less scrupulous masters from freeing older, less profitable slaves as a means of not taking responsibility for them (elderly slaves without employment fell to the care of the state), and at different points states adopted laws compelling freed people to leave their states after manumission.

As far as one's day to day life was concerned, this largely rested on one's credibility with local whites. Although cities such as Baltimore, Richmond, and New Orleans did have larger freed populations, this was not the case everywhere, and free people of color were by no means the majority of the black population in the South. The assumption white southerners operated under was that people of color were slaves. If you were a free person living in a community in which you were known to be free, that was one thing, but traveling from place to place could be tricky, as whites unfamiliar with a given person of color were generally not accustomed to assuming that black people were free.

One of the standard texts on this topic is Ira Berlin's Slaves Without Masters. I can also recommend Brenda Stevenson's Life in Black and White, which deals with these issues as they pertain specifically to the community of Loudoun County, Virginia, and Barbara Fields's Slavery and Freedom on the Middle Ground provides a similar study of the situation in Maryland. Melvin Ely's Israel on the Appomattox provides an interesting account of a specific community of freedpeople in Prince Edward County, Virginia. There's also an older article by Benjamin Klebaner ("American Manumission Laws and the Responsibility for Supporting Slaves, " Virginia Magazine of History and Biography) that also deals with some of these issues.

Again, you can make certain generalizations on this topic, but what you'll find is that a lot of the information on this comes from local studies precisely because these things could vary significantly depending on time and place.