Prayer of a Righteous Man

The Bible says, 

"The effectual fervent prayer of a righteous man availeth much." - James 5:16b 

How can we be righteous? 

"As it is written, There is none righteous, no, not one:" - Romans 3:10 

It is by the gospel - the death, burial, and resurrection of Jesus - and our obedience to the gospel that we can become righteous. (1Corinthians 15:1-4, Acts 2:38).

"For he hath made him to be sin for us [to be the offering for our sin], who knew no sin [who never sinned]; that we might be made the righteousness of God in him." - 2 Corinthians 5:21

When we repent by turning from sin, have our sins washed away by baptism in the name of Jesus, and receive His Spirit in us, through Jesus we are made righteous. We have crucified and buried our old sinful nature and put on Christ. (Acts 2:38, Romans 6:3-6, Romans 14:17).

"For as many of you as have been baptized into Christ have put on Christ." - Galatians 3:27 

Through Christ, our fervent prayers are powerful.

For example,

"And when they had prayed, the place was shaken where they were assembled together; and they were all filled with the Holy Ghost, and they spake the word of God with boldness." - Acts 4:31 (Acts 4:29-31).

"Peter therefore was kept in prison: but prayer was made without ceasing of the church unto God for him." - Acts 12:5 

Peter was miraculously delivered from prison (to the surprise of the praying church). (Acts 12:6-17).

"And at midnight Paul and Silas prayed, and sang praises unto God: and the prisoners heard them." - Acts 16:25 

Paul and Silas were miraculously delivered from prison. (Acts 16:16-40).

A disciple named Tabitha (Dorcas) was sick and died. Peter prayed for her, and she rose from the dead. (Acts 9:36-42).

"But Peter put them all forth, and kneeled down, and prayed; and turning him to the body said, Tabitha, arise. And she opened her eyes: and when she saw Peter, she sat up." - Acts 9:40  

"And it came to pass, that the father of Publius lay sick of a fever and of a bloody flux: to whom Paul entered in, and prayed, and laid his hands on him, and healed him." - Acts 28:8 (Acts 28:7-9).