Here is a good staring point, look unto the Prophets on how they Prayed for God's People.
I believe it isn't the Praying for, it is in the actual carrying the weight of those Prayed for, where God then moves.
Example below.
Dan 9:3-5
3) And I set my face unto the Lord God, to seek by prayer and supplications, with fasting, and sackcloth, and ashes:
4) And I prayed unto the LORD my God, and made my confession, and said, O Lord, the great and dreadful God, keeping the covenant and mercy to them that love him, and to them that keep his commandments;
5) We have sinned, and have committed iniquity, and have done wickedly, and have rebelled, even by departing from thy precepts and from thy judgments:
Jas. 5:16
Confess your faults one to another, and pray one for another, that ye may be healed.
The effectual fervent prayer of a righteous man availeth much.
How fervent are our prayers for God's People?