In Leading in Prayer: A Workbook for Ministers, Hughes Oliphant Old describes the kind of things he did to improve his prayers…
He set aside time to pray. For example, he used Saturday mornings to prepare prayers for Sunday. Similarly, the puritans prayed well because they prayed a lot. They prayed alone, with their families, and in their churches.
He learned through emulation. Like an apprentice painter that learns by first painting the great works of art done by others, Old used prayers he admired from others for his own praying. He used the Psalms and the prayers of the Reformers and church fathers.
Old also practiced his ability to identify the qualities of good prayers (tone, parts, logic, imagery, etc.) and the deficiencies of poor prayers.
Old would also practice by rewriting or reworking prayers to fit modern English and the particular needs of the moment.