Is it a long process or just as simple as me tearing up the paper that says I own him?
EDIT: Thanks for all the amazing answers!
It wasn't a long process to manumit a slave. You went down to the courthouse and declared before a justice of the peace that the person or persons are hereby free. Here is an example. In practice it was far more complicated for the freedman than getting a job and buying a house. Between social and legal factors, most left, at least in the areas I'm familiar with. Here is an example of the legal hurdles they faced.
Archy Lee is worth mentioning in any discussion of antebellum emancipation laws. The patchwork of laws in effect by the 1840s resembled gay marriage laws today: When a slave holder took his "property" to a free state, did the slave gain his or her freedom? And what happened when a fugitive slave ran away to one of these states? Suffice to say it was easier for California's few slave holders to free their slaves than it was in Alabama.
I would like to add to the question. Once freed, how does the former slave prove that he is a freeman, and what risk is there to being captured and sold back into slavery?
I only know about Virginia, but most slave states had similar anxieties about freed blacks which would've led to similar attempts to restrict manumission.
For legal background, private Manumission (that performed by a master) was a legal gray area in Virginia due to the fact that during the colonial period it was seen as a property transaction (transferring ownership of the slave to the slave himself) and one could not legally grant property to an enslaved person. This made it possible for legislature to enact restrictions on the practice.
The free black population of Virginia grew to about 10% by 1800 as a result of manumissions granted to slaves who had fought for the colonists during the revolution, and many of these free blacks advocated abolition which caused problems for those who supported slavery. After Gabriel Prosser's trial in 1800 members of Virginia's General Assembly who opposed private manumission were able to exploit fears of a slave revolt led by free blacks and by 1806 were able to pass an act which required that all slaves freed by their masters had to either leave Virginia within a year or reenter slavery. The law, like several others, was only enforced sporadically and served as a backup to remove free blacks in case they posed a threat.
After this act most of the states surrounding Virginia passed laws restricting the entry of free blacks by the 1820s, making it incredibly difficult for private manumission to occur. There were several ways around this. One way was to petition the Virginia legislature for an exemption allowing one's slaves to settle in Virginia, but these exemptions were granted sparingly after Nat Turner's Revolt in 1831. Another way was the American Colonization Society, which resettled freed black people in a colony in Liberia and was in use from the mid 1820s through the civil war. The Colonization route wasn't an especially popular choice among free blacks due to the uncertainty associated with it, but sometimes it was the only choice available.
sources: what I remember from lectures; John H. Russell, "The Free Negro in Virginia, 1619-1865". If you want to read about a 19th century free black community, I recommend Melvin Patrick Ely and Alfred A. Knopf's "Israel on the Appomattox."
Theres evidence that some more benevolent former masters helped their freed slave by paying the cost of their emigration either to the safety of British Canada or the dubious prospects offered in Liberia.
After the free black population were involved heavily in the Haitian Revolution as well as the slave uprisings in America, as my colleague points out very eloquently there was a fear of emancipated slaves spreading dissent. Oddly in the British colonies the Free Black population were actually very stalwart in being pro-Government and it was free black colonial regiments that put down at least one uprising in Jamaica.
Of course as the 19th century dawned and wore on scientific racism leaked in and became an excuse likewise. If you lived in the South outside of the relatively multiracial New Orleans you never had complete security. Even in many slave states near the border you lived a marginal existence without security and it's fair to say New England (where slavery had never been endemic and was very unpopular by the Jacksonian era, was probably the only real area where you could be reasonably secure of due process etc if arrested as a "runaway" under false pretences. Certainly the Deep South would not be a wise place to be without a white protector, be it a northern lawyer or southern ex master protecting your welfare. Which meant even as a free man you were still reliant in the south on a white benefactor to validate that status and take legal action on your behalf if captured.
David Brion Davis' "Inhuman Bondage" covers the topic in some depth.
George Washington, even as a former President, is a prominent case illustrating the practical difficulties of freeing slaves. As property, slaves were strongly attached to their previous and future owners. A slave owner, Washington eventually changed his views on slavery over the course of his life, and resolved to free the slaves at Mount Vernon. However, some of the slaves belonged to him, some to the estate of his wife's first husband, and many were encumbered as inheritance to the children of her first marriage. He could not free any but his personal slaves without compensating these estates despite his day-to-day power as nominal owner. Perpetually short of cash, he did not manage to do this in his lifetime. The legal story is complicated, though is detailed and noted by the Mount Vernon Ladies Association at: http://www.mountvernon.org/employees-navigation-level-1/encyclopedia-top-level/slavery/george-washington-and-slavery
It varies from state to state and year to year. I'm most familiar with slave laws in South Carolina, so I'll post on that.
After the Revolutionary War, there was a big wave of manumissions in the patrotic spirit of freedom. A lot of people at the time thought that slavery way naturally on its way out. The cotton gin and the massive boom times in the Santee highlands and similar parts of South Carolina put paid to that notion, however, and slaves became incredibly valuable drivers of the economy. That said, you could still free a slave relatively easily, by just going down to the courthouse and getting the papers signed.
All this changed, however, after Vesey's Rebellion in 1822, which made extensive use of freed blacks (Vesey himself was a freed black). Prior to his rebellion, the common wisdom was that only slaves would rebel, as freed blacks "had it pretty well". (He was even interrogated on this point.) After the rebellion, the SC legislature began progressively shutting down the ability to free blacks, eventually banning the practice entirely.
Even as a free black your freedom changed, with the SC legislature eventually requiring all free blacks have a white sponsor or be forced to leave the state. This wasn't especially well enforced, though, and in a lot of areas it was simply ignored. Well to do black people, though, were careful to preserve their legal status and could usually get a white person to sign off on their character.
The ban on manumission became rather problematic, for example, if you were a freed black and wanted to free your wife. So, in another case of the South Carolina citizenry sort of ignoring the law, they would buy slaves they wanted to free, and gave them "orders" to do whatever they wanted. As long as the titular master didn't change his or her mind, they were treated as free blacks even though they were technically slaves.
I recommend reading Black Masters by Michael Johnson on a fascinating freed black who rose from slavery to become one of the richest men in the state, and one of the largest slave owners in South Carolina. (I've visited his house and grave.)
Also Larry Koger's Black Slaveowners goes into a lot of detail on the state of slavery and manumission in South Carolina, and deals a lot with the question of blacks owning blacks, and what percentage of them were simply nominal ownership.
If I may add another question, were slaves United States Citizens that just happened to also be property? If not, when they were freed, did they get their citizenship along with their freedom, or were those two separate processes?