How did King Saul die on Mount Gilboa?

Answer: He fell on his own sword

Critically wounded by archers, Saul asked his armor-bearer to kill him. When he refused, Saul took his own sword and fell on it.

“Now the Philistines fought against Israel, and the men of Israel fled before them, and many fell slain on Mount Gilboa.”— 1 Samuel 31:1 (BSB)