Just like he always has. He is soverign Lord of the universe, and even though it seems that He is silent, has pulled away from being overtly involved in man's affairs, every thing is going as He knew it would.
This is "man's day" (1 Cor. 4:30) designed by God to permit man to discover how utterly foolish it is to attempt to withstand God and His purpose for the ages through His Son, Christ Jesus the Lord.
You ask, "How does God rule?" He can influence the thinking, the decision making of anyone as He sees fit. In so many accounts in the OT, we read of the Spirit of God, or His angels, influencing kings, and others to make certain decisions.
I do not believe He will have a donkey speak like a man to warn someone.
So, those are some of my thoughts.
Bick