One of David's brothers leaves home to meet up with David while he takes his parents to Moab for security.
David is playing it super safe here. Who knows if Saul will go after his family? He could be that crazy. Or evil. Most likely crazy.
A prophet named Gad tells David he needs to find a new hiding place because Saul is getting increasingly more paranoid (1-5).
Saul blames his men for not knowing that Jonathan was helping David. Obviously it's their job to know about Jonathan's life, not Saul's (6-8).
Saul learns that David went to Ahimelech and his sons for help, so Saul sends for them.
When they come, Saul questions Ahimelech because he wants to know why the priest helped David. Ahimelech explains he had no reason to suspect David because he's the king's son-in-law.
Saul doesn't like this answer and orders the priest and his sons put to death. Saul's mercenary herdsman dude, Doeg, does the evil for him. Doeg takes it 100 steps further and slaughters all the women, children and livestock in the town (9-19).
Ahimelech's son Abiathar escapes and joins David. David says that he knew that bad would come from Doeg seeing him with Ahimelech, so he takes responsibility for all of the deaths of Abiathar's family (20-23).