1. Walk, bike ride, or drive to the shrine on a Marian feast day. Make your journey to the shrine a spiritual one, avoiding outside distractions. On the way, pray the Rosary, list your petitions, or offer various other prayers and devotions. 

2. Once you arrive, pay tribute to Our Lady. Remove your caps, greet the Blessed Mother, offer her your gifts (flowers, sacrifices to the Lord, or even your joyful greeting).

3. After you greet Our Lady, pray the Rosary or sing an appropriate Marian hymn.

4. You can offer the Litany of the Blessed Virgin Mary or other prayers as well. 

5. Sing a hymn of farewell once you decide to leave. Such as "Hail, Holy Queen" or "Ave Maria" or something in Spanish or Latin that you may know. The best recommendation is to sing the "Ave Regina Caelorum" which is written in Latin on the dedication plaque. 

6. Finally, give thanks to the Lord for a beautiful journey to the shrine and thank him especially for such a beautiful gift of so noble a mother.