Howard Barnes emphasizes the importance of prayer and worship as great privileges for Christians on earth. Prayer involves various components like intercession, meditation, petition, adoration, confession, and thanksgiving, while worship originates from our connection with heaven. Effective prayer requires persistence, faith, knowledge, holy living, and reverence, and should be addressed to the Father, in the Spirit, and through the Son. Worship involves complete self-diminishing and focusing solely on the worth of God the Father and the Son, seeking true worshippers who worship in spirit and truth.