During the rosary, he or she who prays directs the mind toward two things: 1) the meditation on the particular mystery (or event in the life of Jesus and/or Mary) being prayed ("meditation" as it's practiced in regards to the rosary simply means prayerfully thinking about something) and 2) offering the words of the vocal prayers from the heart.
This requires some discipline. Nonetheless, neither one of these two elements - meditation nor sincere vocal prayer - can be dismissed while praying the rosary. One can imagine the benefit lost by essentially ignoring or performing by rote only one of these two elements. Granted, the Holy Spirit, who plays the ultimate part in initiating our prayer and guiding our meditations, may direct our minds and hearts to one or the other more profoundly as he teaches and sanctifies us through our prayer and meditation. As a rule of thumb, however, we must remember that grace builds on nature, and God usually uses whatever elements of our nature we devote to him that he may enrich us with his grace - this applies no less to prayer.
Both elements of meditating on the mysteries and of saying the words of the Hail Mary's go hand in hand. Especially during the decades of 10 Hail Mary's each, our Blessed Mother's maternal initiative is there to guide our meditation as we open our hearts to praying the words of the Ave Maria with sincerity. Likewise, honest meditation on the mysteries of the rosary - plumbing such theological depths as the Incarnation or in contemplating Christ's face in the Transfiguration - lead us to subject ourselves to the Holy Spirit's inspiration and guidance, and to our Blessed Mother's intercessory mentorship, aware that we by ourselves may only scratch the surface of meditating such mysteries.
Focusing on both elements simultaneously - meaning it as we pray the words of the Hail Mary and meditating on the mysteries - as this demands such discipline, may be made simpler for us by using certain methods. St. Louis De Montfort suggested that one focus on one idea - or point - of meditation for each Hail Mary prayed during the rosary. For example, while meditating on the Nativity, one may think about the hardship Mary and Joseph endured while traveling to Bethlehem while praying one Hail Mary, then while praying the next Hail Mary, meditate upon their finding a stable and preparing for our Lord's birth. Such simple points consisting of a single idea each simplify the meditation and allow one to focus in the "mind's eye" on that one idea while simultaneously praying and offering from the heart the words of prayer to our Blessed Mother. And, although each Hail Mary is accompanied by a single thought from the mystery, upon meditating on one such point for each of the 10 Hail Mary's in a decade, one ends up with a pretty thorough meditation on any particular mystery.
The method I describe is not necessary for praying the rosary. Indeed, one may meditate upon a single point throughout all 10 Hail Mary's throughout a decade if desired. However, this is a method I have personally found helpful, and is one I usually find myself returning to after realizing how slipshod and distracted my meditations can be when I don't apply as much discipline or any particular method to them. The method I expound and the ideas behind it, consequently, are those on which the scriptural rosary is based.
The scriptural rosary offers a single verse from scripture, which hopefully faithfully represents the mystery and offers a single yet substantial point to meditate on, to be prayed during each Hail Mary. Below please find the Scriptural Rosary I am presently composing for an example. Better yet, go ahead and pray a couple decades of the rosary using it. God bless.