Many different particular methods were used to subjugate an entire race of people at the whim of another in American History. Most of these methods revolved around oppression and an extreme denial of voice. Violence, as alluded to in the previous post, was one of these means. At the same time, isolating one slave and demonstrating the harshest of cruelty was employed as means to send a message to others. With the passage of the slave codes, slaveowners were given more latitude in controlling their slaves through use of violence and even being able to escape legal ramifications for murder. Subtle, yet equally effective cruel, means of control was also offered. For example, denying education to slaves kept them in a form of mental bondage, allowing for a greater sense of control to emerge. At the same time, slaveowners breaking up families were used to control slaves, as it helped to break one's spirit. Finally, many slave owners resorted to "divide and conquer" methods of control, where specific and "chosen" slaves were given marginally better treatment over others. This helped to prevent any notion of cohesion amongst slaves, resulting in a greater sense of control.
Clearly, all of the above answers are right, but there are a couple of important things that none of the three previous answers has mentioned. The previous answers all focus on coercion and brutality. But much of the control of slaves was based on much more subtle things.
First, the slaveowners used (or tried to use) religion to control slaves. They encouraged slaves to believe in a version of Christianity that emphasized obedience. They encouraged the slaves to think of their rewards in the afterlife, not of their problems in this life.
Second, they did not allow slaves to learn to read or write. This was partly meant to prevent them from reading about ideas of universal rights and things like that. But it was also to prevent them from having the tools needed to start rebellions.
Finally, they used psychology, at least with some slaves. Some masters treated some slaves with something approaching respect -- gave them high responsibilities and such. This could create something like loyalty in those slaves.
I'm not saying brutality wasn't used. But the more subtle things are just as effective, if not more so.
There were many different types of approaches to control slaves in the U.S. - from the physical to the psychological. Here are a few examples. If you beat someone or threaten someone with physical punishment, then this is a strong type of control. The mere threat is strong on a emotional and psychological level, which cannot be ignored. What makes things even more cruel is when a slave had a family. Now the slave not only has to worry about himself, but he also has to worry about his family. This was a powerful type of control. There were other approaches as well, such as changing slave names to Americanized names to change their identities. If you think about it a little, I am sure that you can come up many more.
Cruelties practiced against slaves, were one of the methods of controlling slaves, through whippings, mutilations and families splitting.
Another method of controlling slaves was to introduce the idea of racial difference and inferiority, black persons being considered inferior and dependent race. Among the concerns of the South were not only economic losses but also fears of racial equality. Texas Declaration of Causes of Secession specifies the fact that non-slave states "proclaim humiliating the doctrine of equality of all people, regardless of race or color". Alabama secessionist E.S. Dargan said that emancipation would make Southern people feel "demoralized and degraded".
In addition to the methods of torture, both physical and psychological, another way of control was just the law itself. As proof lies "Law of Fugitive Slave" , issued in 1850 and cited in the "Declaration of immediate causes which produce and justify the Secession of South Carolina", from the Federal Union, of 24 December 1860.