One of the most important things we do as Christians is pray for those who are not Christians yet.
How do we pray effectively the salvation of lost people?
Check your motivation
Your motivation should be the glory of God. I understand you cannot help wanting to see your husband come to Christ for the benefit of your marriage, or your children come to Christ for their own good. But that should not be your chief motivation in praying for them. Our primary desire is to see Christ glorified through their salvation. One day all the redeemed will stand before His throne worshipping Him (Revelation 5). Pray that God will multiply the praises coming to His Son by adding a new voice to that heavenly choir!
Check your faith
Jesus said: "Therefore I tell you, all the things you pray and ask for--believe that you have received them, and you will have them" (Mark 11:24). I take this to mean that when we pray for people to be saved we should believe that God has already saved them. Visualize them in that heavenly choir!
Pray for conviction of sin and lostness
One of the reasons many people do not come to Christ is their lack of need. They believe they are already "good enough to go to heaven." Their self-righteousness gives them a false sense of security. It is like a ship-wreck survivor trusting in his life vest to save him in northern Atlantic. They won't last ten minutes in those ice-cold waters! Before we will come to Christ for salvation must first be convinced that "we need savin'." This is the Holy Spirit's area of expertise. His job is to "convict the world of sin, judgment and righteousness" (John 16:8). The Holy Spirit shows us the truth about ourselves: that we are sinners, and our sins separate us from a holy God. Pray that the Holy Spirit will show them their need for a Savior--and that Jesus Christ is the only qualified candidate for the job!
Pray for deliverance from Satan and his arguments
Yes, Satan does have a grip on them and he does not let go without a fight. Pray that the obstructing thoughts he has placed in their minds will be torn down, and their thoughts will be brought captive to obedience to Christ (2 Corinthian 10:5).
Remind God of His love for them
This is something that David never ceased to do. He was a "man after God's heart," but he constantly reminded God of His promises. We do not remind God of His promises because He is prone to forget, or in an attempt to twist His arm. We do not manipulate God or make demands of Him. But, like His trusted servant David, we should remind Him of His faithfulness to His Word and His love for people. After all, it was to "seek and save the lost" that Jesus came down from heaven (Luke 19:10).
Don't give up!
Sometimes it takes years--not because God is weak-- but because people are so stubborn. I do not wish to insult anyone's theology, but people do have a free will. God will not force His will on people. It is a testimony to the strength and wisdom of God that He can give man a free will without compromising His sovereignty. It is also a testimony to His patience that He labors long over us. God does not give up on us, so we should not give up on others. Keep praying. "And let us not grow weary of doing good, for in due season we will reap, if we do not give up" (Galatians 6:9).