First of all, congratulations on getting such a beautiful medal! Have it blessed by a priest, and then wear it in whatever way suits you - either round your neck on a chain or cord, or in a pocket or some other way. I wear mine on a cord round my neck.
Did you get an explanatory leaflet with it? It’s very important to know the history of it and why we wear it.
Basically Our Lady appeared to St Catherine Laboure in 1830 and asked her to have this medal struck and promised that whoever wore it would obtain many graces. Now this doesn’t mean it’s a lucky charm, but that by meditating on the symbols on the medal we are drawn deeper into prayer and contemplation of the mysteries of salvation.
The front of the medal shows Mary, standing on a globe of the world, crushing the serpent beneath her feet. She is holding out her hands and rays are coming from them, representing the many graces she has been appointed to give us. Around her are the words of the prayer: “O Mary, conceived without sin, pray for us who have recourse to you.” On the reverse of the medal, You’ll see a large M, at the foot of a Cross which has a horizontal bar at the base. This represents Mary at the foot of the Cross, and reminds us that she is forever linked to the passion of Our Lord and stands there as our representative. Below this are the two hearts: the one on the left is the Sacred Heart of Jesus, all aflame with love for us, and the one on the right is the Immaculate Heart of Mary, pierced by a sword as Simeon told her. Around the edge are twelve stars, for the twelve apostles.
I hope you receive many graces while wearing it, and that it helps to deepen your faith.