I have already recommended to you Donald Whitney's book Praying the Bible. Here is a brief video in which he explains how to pray the Bible. As he says at the end of the video, try it yourself! Even if you understand what this means conceptually, you won't understand its effectiveness and power until you try it.
The Bible has often been described as a letter from God to his people. One important difference between a letter and the Bible is that we usually write letters to people who are not with us. We figure that if we are with someone we don’t have to write, we can just say what we want to say. But when we read the Bible, we are reading what he has written to us and we are with him! The Bible is part of our conversation with God. As mentioned above, the Spirit of God is present, helping us understand and apply what the Bible teaches.
When we pray the Bible, we respond in prayer to what we are reading. We listen to what the Spirit is saying to us and how he leads us in prayer as we read Scripture. We are participating in a conversation with God.
Praying the Bible is an important concept to understand because we so easily make Bible reading an intellectual exercise. That is, we are only using our brains to figure out what the words are saying. Reading the Bible certainly includes using our brains, but it is much more. If we turn Bible reading into only an educational or intellectual exercise, instead of a personal conversation with God, then we have missed its fundamental purpose. This is what Jesus said to the religious Jews,
“You search the Scriptures
because you think that in them you have eternal life;
and it is they that bear witness about me,
yet you refuse to come to me that you may have life.”
So, what does it mean to pray the Bible? Praying the Bible means immediately responding to the words and ideas in the Bible through prayer. Talk to God about what you are reading. Be sensitive to the ways that God is speaking to you through the Scripture and respond to what he is saying and bringing to your mind. What you read might even trigger a thought that does not seem to be directly related to the Scripture. You can pray about that too.
You can learn more about this kind of conversation with God in the book Praying the Bible by Donald S. Whitney.