As a noob Catholic, I would covet some advice from those who are more mature in the Faith: how would one go about becoming closer to the Blessed Virgin?
A good start would be praying the Rosary.
Here is a web site that gives information on the Rosary.
http://www.rosary-center.org/nrosary.htm
Peace
I recommend reading the references to her in the Bible and contemplating any connection you see between you and her.
I never thought I had much in common with Mary, since I was well-educated and single until age 34. But then I had my first child, and Christmas came soon thereafter, and I heard the Gospel reading of the Magnificat (”my soul magnifies the Lord”) and also the little phrase “Mary pondered all of these things in her heart.” I realized she was a thinker, with a strong mind of her own, not just blindly obedient.
She knew her scripture. According to a Protestant friend of mine, the Magnificat text harkens back to prayers of other OT women (although I can’t remember who).
She also could tell Jesus to get busy and help out (wedding at Cana), and He did. He called her “Woman”, not “mom” because the translation is a special term that is more like “THE Woman— the preeminent Woman”. This event is where people get the confidence to ask Mary for intercession. A regular guy mentioned to her his problem, and she, The Woman, went to bat for him right away.
People can argue that you could just ask Jesus directly, and you can, but Mary has been bugging her Son about the real-world problems of ordinary people for some time now, and it keeps working. So people keep doing it.
Welcome to our Church. Have fun on your journey!
Pray the Rosary. The rosary of the day is posted every day in the Daily Readings thread.
Learn the Memorare
Sing Immaculate Mary for a day — they sing this at Lourdes in the procession.