The word, slave, is only used two times in the King James Bible: Jeremiah 2:14; Revelation 18:13. However, often (though not always) when the word "servant" is used it carries the meaning that we would apply to slave. For instance, Genesis 20:14 tells how Abimelech took "menservants, and womenservants, and gave them unto Abraham." These servants were not free. They were given to Abraham as the sheep and oxen were given.
The curse of Noah on Canaan in Genesis 9:25-27 says of Canaan: "Cursed be Canaan; a servant of servants shall he be unto his brethren." He is to be a servant to Shem and a servant to Japheth, his father's two brothers. However, this is not a clear slave-master relationship. This passage has been interpreted in many ways. The idea that Canaan was an actual slave to Shem and Japheth is probably much less likely than several other choices.
The first definite slave-master relationship I can find is in Genesis 12:16 where Abram (later called Abraham) has menservants and maidservants. Abram was definitely a slave-holder. The first time I can find where we know both the name of the master (or, in this case, the mistress) and the slave is in Genesis 16:1 - "Now Sarai Abram's wife bare him no children: and she had an handmaid, an Egyptian, whose name was Hagar." Sarai (later called Sarah) is the mistress and Hagar, who was the mother of Ishmael, was the maid or slave. The relationship is described as one in which Sarai "dealt hardly" (Genesis 16:6) with Hagar and later told Abraham, "Cast out this bondwoman" (Genesis 21:10)