How to pray and meditate while saying the rosary? What to think about when praying the rosary? If one thinks about the mystery (e.g. sorrowful mystery) while praying, then one can not pay attention to the words of Hail Mary but if one concentrates on Hail Mary then one can not meditate the mystery. How to pray the rosary properly, ie. in a way that one concentrates both on the Hail Mary and on the mystery?
I would prefer examples from the lives of saints and an explicit answer to my question from saintly authority (because it is impossible that no one asked this question before). Thanks.
The Handbook of Prayers contains a number of meditations written by St. Jose Maria Escriva which put you and him in the place where Jesus and Mary are in that particular mystery.  It is a lot like the Stations of the Cross in that regard, where in the short meditation, to be read before each decade, St. Jose Maria explains the feelings and thoughts a person might have when experiencing the things that Scripture and Tradition say happened during the events in the mysteries.
If you want to go even deeper, there is a meditation published on CatholicTradition.org which goes bead by bead which is adapted  from Ven. Mary of Agreda's work &quot;City of God&quot; (a work detailing visions she received).
However, neither of these have the Luminous Mysteries.

As for the Saint's who have given their input into the matter of the Rosary, there's no better work than St. Louis De Montfort's The Secret of the Rosary which you can also find on CatholicTradition.org (or at TAN books).  It's got writings from Bl. Alan De La Roche who revived what St. Dominic was handed from Our Lady herself. He also received visions and messages from The Virgin Mary on how and why to meditate on the mysteries of the Rosary:

She also taught it to Blessed Alan de la Roche and said to him in a vision: &quot;When people say one hundred and fifty Angelic Salutations this prayer is very helpful to them and is a very pleasing tribute to me. But they will do better still and will please me even more if they say these salutations while meditating on the life, death and passion of Jesus Christ----for this meditation is the soul of this prayer.&quot;

But you're right, it is difficult to discern when you're meditating on the words and when you're meditating on the mysteries.  Because St. Louis also wrote this, concerning the Our Father:

People who say Our Lord's Prayer carefully, weighing every word and meditating upon it, may indeed call themselves blessed for they find therein everything that they need or can wish for.

Nevertheless, it would seem that mediating on the Lord Prayer inbetween the mysteries is more important and that Bl. Alan also says that you can't possibly fathom the meaning of &quot;Hail Mary&quot; so it's a mystery within a mystery.  The best advice I can glean from The Secret of the Rosary is that the meditation on the Hail Mary beads is mystery-related and the meditation between is on the meaning of the words of the Lord Prayer and other prayers.

Having attempted to put some of the word of St. Louis De Montfort into practice in praying the Rosary lately has greatly improved my understanding of what it means to pray the mysteries.  There are several sections in the Secret of the Rosary which break down the parts of the Hail Mary and the Our Father.  I believe the key to your question is in there.  It's not the individual words themselves, but the parts of the prayer in reference to the mystery.  The Hail Mary consists of two parts, the praise part and the petition part.  So in reference to the mysteries of the Rosary, one can praise Our Lady with the frame of reference being the backdrop of the mystery you are mediating on, then ask her intercession with that same backdrop.
In any event, here is one more resource that could come in handy, St. Louis apparently taught many ways of praying the Rosary, so you might be be able to have your cake and eat it too, just not at the same time.