Although God broadly worked with the family of Abraham, the most important line of descent was through his second son (but first by Sarah), Isaac. Even though Ishmael was his first son (through a servant woman named Hagar), God considered Isaac the firstborn as far as receiving the birthright blessings (Genesis 17:19, 21:12. 25:5). Although Abraham himself was circumcised (Romans 4:9 - 12) he was not a Jew.
Isaac had two sons named Esau and Jacob (Genesis 25:24 - 28). After deceiving Isaac in order to get the birthright blessing, Jacob left to live with and work for Laban, his uncle (mother's brother, see Genesis 28:1 - 2, 5). Jacob married the two daughters of Laban, Leah and Rachel (Genesis 29:15 - 30). Jacob later had altogether 13 children, of whom the 12 sons became the names of the tribes of Israel. Jacob himself was renamed "Israel" by God (Genesis 32:27 - 28) after struggling with a Messenger from God (the Father) who later became Jesus. The name "Israel" in the Bible generally refers to all the people descended from the twelve tribes and not just one tribe (e.g. Judah).
Strictly speaking, the term "Jew" applies to the descendants of Judah, who was the fourth child born to Leah and Jacob. Judah means "praise" in Hebrew (Genesis 29:35). Judah is the first person that can be considered Jewish.
After King Solomon's death, however, there was a split between the northern kingdom of Israel, which established a new capital at Samaria, and Judah, which had its capital at Jerusalem. Historically, the tribe of Benjamin stayed loyal to the dynasty descended from King David that still ruled from Jerusalem. Additionally, most of the priestly tribe of Levi moved out of the northern kingdom in order to avoid worshipping the newly created false gods established at Samaria. Because these two other tribes aligned themselves with Judah, people descended from them are also considered in the Bible to be Jews.
It should be noted that gentiles (non-Israelites) become a Jew spiritually, by faith, even when they are not circumcised (Romans 2:28 - 29).