David's story is told across 1 Samuel, 2 Samuel, 1 Kings, and 1 Chronicles. Many of the Psalms are ascribed to him.
Traditional attribution: Many of the Psalms are traditionally attributed to David (Wikidata Q41370).
Key passages:
"Then Samuel took the horn of oil, and anointed him in the midst of his brethren: and the Spirit of the LORD came upon David from that day forward. So Samuel rose up, and went to Ramah." — 1 Samuel 16:13
"Then said David to the Philistine, Thou comest to me with a sword, and with a spear, and with a shield: but I come to thee in the name of the LORD of hosts, the God of the armies of Israel, whom thou hast defied." — 1 Samuel 17:45
"And thine house and thy kingdom shall be established for ever before thee: thy throne shall be established for ever." — 2 Samuel 7:16
"The LORD is my shepherd; I shall not want." — Psalms 23:1
Read the full narrative in 1 Samuel and 2 Samuel, and the songs attributed to David in Psalms.