The keys to praying for others can be found in the words of Jesus and Paul.
1. Pray that God would send laborers into their lives who would transmit the gospel in a way that is relevant to them. It is the Word of God that opens the hearts and transforms them.
"Then saith he unto his disciples, The harvest truly is plenteous, but the labourers are few; 38 Pray ye therefore the Lord of the harvest, that he will send forth labourers into his harvest." (Mt. 9:37-38)
2. Pray that the Word would reach their heart and reveal God's love. The revelation of God's love is the most important revelation that one can receive. Love this person with the love of God.
"For this cause I bow my knees unto the Father of our Lord Jesus Christ, 15 Of whom the whole family in heaven and earth is named, 16 That he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man; 17 That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, 18 May be able to comprehend with all saints what is the breadth, and length, and depth, and height; 19 And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God." (Eph. 3:14)
3. Pray that the Spirit would convict them of their need and the gift of righteousness. This is not a condemning conviction, but a revelation of their ‘lostness’ and that Jesus is the answer.
"And when he is come, he will reprove the world of sin, and of righteousness, and of judgment: 9 Of sin, because they believe not on me;" (John 16:8-9)
4. Pray that the seed of the Word that already exists in their heart, or that will be heard by them, will spring up and grow in their life. Believe that the Word of God will transform their heart and mind.
"And he said, So is the kingdom of God, as if a man should cast seed into the ground; 27 And should sleep, and rise night and day, and the seed should spring and grow up, he knoweth not how 28 For the earth bringeth forth fruit of herself; first the blade, then the ear, after that the full corn in the ear 29 But when the fruit is brought forth, immediately he putteth in the sickle, because the harvest is come." (Mark 4:26-29)
5. Pray that they would have a revelation of God’s goodness. It is His goodness that leads us to repentance.
"Or despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance?" (Rom. 2:4)