(Today's passage covers David and his crew running away from Saul, and Saul pursuing them.)
You've got to hand it to David; he's one sneaky guy. Over the course of these four chapters, he successfully scams a bunch of people and smooth-talks his way into getting an apology (yes, again) from Saul.
To start at the beginning. When last we left our intrepid hero, he'd just kissed goodbye to his best friend, Saul's son Jonathan, and ran off. Now, imagine you're David: you're alone, hungry, weapon-less, and the king is after you. What do you do? Well, the first thing to do is procure some food and a weapon. David chooses to do this by tricking Ahimelech, a priest. He tells him that he's on a secret mission for Saul, and that he needs food and a weapon. (In Judaism, this sort of move is called "chuzpah." In Mexico, you might say he's got cojones the size of elephants.) Ahimelech is completely taken in, gives David a bunch of consecrated bread and Goliath's sword, and that is that. (1 Sam. 21:1-9)
But that is not that. Because it looks like one of Saul's servants, Doeg, also happened to be at Nob when David was speaking to Ahimelech and saw the whole thing. So when Saul is bemoaning that his servants have all betrayed him (he's getting a bit paranoid in his old age), Doeg pipes up and mentions the encounter. (1 Sam. 22:6-10)
Saul summons Ahimelech and condemns him as a traitor. Ahimelech argues in vain that he had no idea what was going on -- after all, David is the king's son-in-law and a loyal member of his household -- but this isn't good enough for Saul. He orders his men to kill Ahimelech and the other priests. They, sensible God-worshippers, refuse. So loyal Doeg kills 85 priests and destroys every man, woman, and child in Nob, just for good measure. The only escapee is Ahimelech's son, Abiathar, who hides out with David. (1 Sam. 22:11-23)
David, meanwhile, has been gathering his own little band of misfits, about 600 debtors and discontents. He saves the town of Keilah from the Philistines, but they threaten to give him up to Saul, so he runs away. In fact, he does a lot of running away, all while Saul is right on his heels. In the wilderness of Maon, David is camped on one side of a mountain, and Saul on the other. David escapes by the skin of his teeth when Saul is suddenly called away to fight yet more Philistines, otherwise the story might have ended a lot differently. (1 Sam. 23)
How does the story end? Saul choses to (ahem) relieve himself in a cave, the very same cave David and his men are hiding. David's men goad him to kill the king, but instead he sneaks forward and cuts off a bit of Saul's robe. When Saul leaves, David rushes forward and announces what he's done, brandishing the robe scrap as proof. He had Saul in his clutches, but let him live, proving that he's not the king's enemy. Saul sees the error of his ways, asks God to bless David, and finally acknowledges that David will be king. He asks David to swear that he won't kill Saul's descendants in the aftermath, which David does. (1 Sam. 24)
And that, as they say, is that. At least until Saul decides to go back on his word... again.