Chances are you've noticed that there are some missing words here and there in your text. That's due to the Bible being, you know, ancient, sometimes things get lost in time.
This is one of those times. Long story short, the age Saul started to reign, but for exactly how long he did reign is lost to us. Oh well, let's move on (1).
Saul and his son Jonathan are out fighting the Philistines. Jonathan defeats a group of them and tensions rise.
The Philistines gather a large force for battle, but the tribes of Israel are afraid and most people hide. Saul gets nervous and summons Samuel to the battlefield to make an offering to God.
Not arriving when he should Saul makes his own offering (a big no no). Naturally, Samuel arrives just after the sacrifice because that's how the world works (2-10). Murphy's law and whatnot.
Saul tries to explain the situation to Samuel, but he only responds by saying that God will now take the kingdom away from Saul. This seems pretty harsh, but you know what, Saul kind of stinks at his job anyway (11-14).
Samuel takes off, leaving Saul with only 600 men. It looks like the Philistines will quickly demolish the Israelites.
Because there are no blacksmiths during this time, Saul and Jonathan are forced to have the Philistines sharpen their weapons for a large fee before the fight (15-23).