The only way I know of getting very close to Our Lady is to pray her rosary. So from now on I will try to pray it more often throughout the day.
The Rosary will be a very powerful armor against hell; it will destroy vice, deliver from sin and dispel heresy.
The rosary will make virtue and good works flourish, and will obtain for souls the most abundant divine mercies. It will draw the hearts of men from the love of the world and its vanities, and will lift them to the desire of eternal things. Oh, that souls would sanctify themselves by this means. - Promises of Our Lady to Christians who pray the Rosary
If by chance your conscience is burdened with sin, take your Rosary and say at least a part of it in honor of some of the mysteries of the life, passion, and glory of Jesus Christ, and you can be sure that, while you are meditating on these mysteries and honoring them, he will show his sacred wounds to his father in heaven. He will plead for you and obtain for you contrition and the forgiveness of your sins. One day our Lord said to Blessed Alan, "If only these poor wretched sinners would say my Rosary often, they would share in the merits of my passion, and I would be their Advocate and would appease the justice of God." - Secret of the Rosary