Samuel anoints Saul privately and tells him what will happen in specific detail in the next few days. He is to wait at Gilgal for Samuel for 7 days. Saul prophesies with a group of prophets, but doesn't tell his family about it or about his anointing. Samuel inaugurates Saul publicly at Mizpah - some don't support Saul.
The Ammonites besiege Jabesh Gilead, but give them 7 days to seek help from Israel. Saul raises the army and defeats them. Israel celebrates and confirms Saul as king at Gilgal.
Samuel says farewell to Israel, asking if he's wronged anyone. He retells their history and calls down thunder and rain to instill reverence in them for the Lord. Israel admits they did wrong to ask for a king. Samuel assures them of pardon from God.
How this is about Jesus
Jesus is anointed King of Israel by the Spirit at His baptism.
He also is approved by the people for a time, after visible victories of healings.
He leads us to repentance and deals mercifully with us afterward (His restoration of Peter, e.g.).
God knows what will happen to us specifically in the next 36 hours (ch. 10)
When God's people call for help, respond and help them! (ch. 11)
Keep short accounts of reconciliation so that no one can accuse you of offense or injustice (ch. 12)