1. Walk, bike ride, or even drive (if necessary) to the shrine on Friday (at any time of the day or night). Make your journey to the shrine a spiritual one (don't listen to secular music or books). 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. Since the shrine is dedicated to Our Lady as Queen of Heaven, and since it is Easter, pray the Glorious Mysteries of the Rosary. 

4. You can offer the Litany of the BVM or other prayers as well. Since it is First Friday you can pray the Litany of the Sacred Heart of Jesus or even the Divine Mercy Chaplet in addition to your Rosary.

5. Sing a hymn of farewell once you decide to leave. I'd suggest "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. It is a hymn, you can youtube it and sing along. 

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.