The Jews, as a people, come into existence after the return from exile in Babylon in c. 539 BCE. Before that, they are Judahites and Israelites. It's an easy distinction to miss, but there IS a difference. I've heard the ancient Israelites referred to as Jews a few times lately from pulpits (I listen to podcast sermons, not just my local pulpit, so no indirect finger pointing). The "Jews" did not leave Egypt with Moses, conquer Canaan, and establish the kingdom of Israel. (I realize Jewish tradition, esp. the Passover haggadah, links ALL Jews to the experience of Exodus. That's a theological issue, not a historical one.)
After the kingdom splits in two (under Rehoboam, Solomon's inept son), the two kingdoms are Israel and Judah. The inhabitants of the northern kingdom were Israelites, not Jews. The inhabitants of the southern kingdom were Judahites. Both peoples are ancestors of the Jews. After the northern kingdom was taken into exile in 722 BCE, the southern kingdom received a large population bump, so Judah under Hezekiah and the following kings until the exile probably included tribes of Israel and Judah together.
If you're reading Ezra, Nehemiah, Esther, or the New Testament, the people are Jews. If you're reading the books of Samuel, Kings, or most of the prophets, they're not Jews. Better to refer to them as Israelites when unified or in reference to the northern kingdom (Elijah was a northern prophet, for example). Referring to the people of the southern kingdom as "Jews" would be marginally acceptable. For a good discussion of the transition from Israelite to Jew, listen to Michael Satlow's podcast series "From Israelite to Jew" found on his blog or through iTunes.