There were two different ways of becoming a slave. In one group there where slaves who had lost their freedom due to there own fault. Most of the time they had committed a crime or something like that. - The other group were prisoners from combat and a lot of poor people who most of the time worked for the rich families in the villages in which they lived.
When the Europeans discovered America in 1642 they started a civilisation there, but in order to build all the buildings and to do all the work done they used slaves. In the first place they took native Americans who already lived there, but they mostly ran away or died because of the 'strange' diseases that the Europeans introduced to America.
So Europeans had to find other slaves and they started taking people from Africa and transporting the slaves to America to work from them. A lot of slaves where deported this way by - the French, English and Dutch people.
Some people started to work as slaves for others because they had to pay them money back or other such situations. They were freed after a period of work and went on with their normal life. When a slave gave birth to a child, the child automatically became a slave too i.e. they were born into slavery. These were the most common ways of becoming a slave.