The Israelites were wrong in asking for a king. After all, God was their king, so choosing a human king pretty much told God where they wanted him to go.
God is gracious and compassionate, and he lets the Israelites have a king: Saul. Through Samuel, he told the people (and Saul) that as long as they obeyed the Law then God would work through Saul and his special people, Israel, to be his representatives in the world.
Saul couldn’t do it. These stories account his failure to obey the Lord.