I suspect that one way to improve the quality of GROUP prayer times is to encourage strong personal devotions.  This is based on listening to wise brothers and sisters at our morning prayer time or at leadership meetings or during worship services.  I can hear influential scripture passages in many of the prayers offered.  Phrases are pulled from God’s promises, Paul’s prayers, Jesus’ discourses, the Psalms, and many other verses into a flow of adoration, thanksgiving, and requests. 

Four things that may help build stronger personal and group prayer:  (1) Start a Bible reading time by asking God for more facility in prayer.  (2) While reading any scripture passage, look for ways to pray the words back to the God who wrote them. (3) Pray aloud in personal devotions, consciously speaking complete sentences. (4) Practice. 

Additional items added 8/27/14:

(5) Read the prayers in scripture, capturing the ideas and learning from them

(6) Memorize the words of scripture to pray them

(7) Pray with your spouse or other belivers during devotion time

(8) Sing psalms / hymns / spiritual songs and use them as prayers