I should probably write an entire story about this as I have been meaning to. I used a book called "33 Days to Morning Glory" by Michael E. Gaitley to prepare for mine but it's a 33 day process where at the end you can make vows to Mary.
What started my relationship with Mary was praying the rosary, and as someone who wasn't Roman Catholic (I do say I'm Anglo Catholic, best of both worlds, as in I'm deep on the Catholic side of the Episcopal Church. Clear as mud)? Ha.
I asked what most people who aren't Catholic asked and that is why pray the rosary with the Hail Mary when we should pray to Jesus. The friend who taught me to pray it said "because Mary leads us to her son." That actually made a lot of sense to me as someone with mother issues.
Anyway what it's really about is building a relationship with Mary. I wrote my own vows because I do that kind of thing. Anyway, feel free to ask if you want to know more. I should probably write a whole post. Some people might be interested, who knows.