Slavery in America began in 1619, meaning that was when slaves began to show up in the original colonies. However, this practice had happened even in the Spanish colonies as early as the 1560s.
What has to be remembered is that slaves weren't always the way we think of them. Sometimes slaves were indentured servants, meaning they were people who sold themselves into servitude for a predetermined period of years (for example seven or fourteen). This was done in exchange for passage to America, and a place to live while working for their master. When the period was up, that person had earned their freedom, even though there was the Fugitive Slave Act in 1850, stating you had to return any fugitive slave to their owner.
There were, of course, what we traditionally think of as slaves. There were slaves that had been brought over from Africa, after having been bought or kidnapped. There were tribes that would kidnap members of other tribes to be sold to white people to be brought over to America and sold into slavery.
There was eventually a ban placed on moving new slaves into America. This meant that you could no longer go and purchase one off of a boat. Any slaves that were sold had to be born from slaves that were already in America. The laws that governed this were complicated as well.
By 1860, there were more than four million slaves in America.