We pray with Mary and We ask Mary to intercede for us.
When Catholics pray to God they "utter a petition to God." When they pray to Mary and the Saints they are making a "devout or earnest request for" prayers from Mary or the saints.
In the book, A Man of Faith about Father Patrick Peyton, written by Jeanne Gosselin Arnold, it is summed up simply:
The difference is not in what God can do and what Mary can do. The difference is in the way they do it. God wills something and it happens. Mary prays to Him for something and He does it. He will never say 'no' to her.
- Father Cornelius to Father Patrick Peyton in A Man of Faith by Jeanne Gosselin Arnold
Therefore when we “pray” to Mary we are asking her to pray for us and with us.
We say, “Hail Mary, full of grace, the Lord is with you. Blessed are you among women and blessed is the fruit of your womb–Jesus. Holy Mary, Mother of God, pray for us now and in the hour of our death. AMEN” The prayer itself is simply a request that she pray for us.