Rex B. Andrews preaches about the transformative power of prayer, emphasizing the importance of shifting our focus from self-centered desires to God-centered purposes. He highlights the need to acknowledge our spiritual poverty and surrender our will to God, allowing Him to work in and through us. Andrews explains that true prayer involves a process of self-emptying and seeking God's will above our own, leading to a deep dependence on God's grace and mercy for sustenance and strength in the face of life's challenges.