Adam Clarke on 1 Samuel 10:1

Took a vial of oil - The reasons of this rite the reader will find largely stated in the note on Exo 29:7. The anointing mentioned here took place in the open field. See the preceding chapter, 1Sam 9:26-27 (note). How simple was the ancient ceremony of consecrating a king! A prophet or priest poured oil upon his head, and kissed him; and said, Thus the Lord hath anointed thee to be captain over his inheritance. This was the whole of the ceremony. Even in this anointing, Saul is not acknowledged as king, but simply נגיד nagid, a captain - one who goes before and leads the people.