The power described by Joseph Smith was the influence of the Holy Ghost. As a result, Joseph went into a grove of trees near his home and knelt down to ask of God. The First Vision that followed was truly momentous and magnificent. But the path to that in-person visitation of the Father and the Son began with a prompting from the Holy Ghost to pray.
The revealed truths of the restored gospel came through the pattern of seeking in prayer and then receiving and following the promptings of the Holy Ghost. Consider these examples: translating the Book of Mormon; the restoration of the priesthood and its ordinances, beginning with baptism; and the organization of the Church—to name a few.
I testify that today, revelation from the Lord to the First Presidency and the Twelve comes according to this same sacred pattern. This is the same sacred pattern that allows personal revelation.