Being king, Saul would have had many lookouts and men available to him. The fact that David had left the court and was being sought by Saul would have quickly become common knowledge in the area around Gibeah. With people travelling between Gibeah and Ramah, someone who saw David would have simply passed the information on.
19 And it was told Saul, “Behold, David is at Naioth in Ramah.”