Samuel privately anoints Saul and gives three signs

Private speech, a vial of oil, and a kiss

When they are come down from the high place into the city, Samuel communes with Saul upon the top of the house. At rising, about the spring of the day, Samuel calls Saul to the top so he may send him away. As they go down toward the city, Samuel tells the servant to pass on before them. Then Samuel takes a vial of oil, pours it on Saul's head, kisses him, and says, is it not because the LORD has anointed thee to be captain over his inheritance?

The unit crosses a chapter boundary. Textual witnesses vary in parts of the anointing speech. Private designation is clear. Anointing does not create a ritual for selecting modern rulers.

Three signs, another man, and a commanded wait at Gilgal

When Saul is departed from Samuel, he will find two men by Rachel's sepulchre who will say the asses are found and that Kish now sorrows for his son. Then three men going up to God at Bethel will meet him with kids, loaves, and wine, salute him, and give him two loaves. Then at the hill of God, where there is a Philistine garrison, a company of prophets will come down with psaltery, tabret, pipe, and harp, and they will prophesy. The Spirit of the LORD will come upon Saul, he will prophesy with them, and he will be turned into another man.

'Another man' concerns changed capacity for this royal-prophetic moment, not loss of identity and not a clinical state. Saul is to do as occasion serves him, for God is with him. Then he must go down before Samuel to Gilgal and tarry seven days until Samuel comes to offer and to show him what to do. Signs confirm; they do not guarantee moral transformation, and they do not authorize acting on impressions without the given instruction.