What is it?
Consecration to Mary is not to be taken lightly. It is a lifelong commitment to serve Our Lady in all of the many ways that we can. It is a promise to be Mary's servant, to think nothing of ourselves or what we will get out of it, and most importantly, it is the most perfect way for us as Catholics to get close to Jesus. Jesus can refuse Mary nothing. He is completely enslaved to do her will, but Mary will not ask Jesus to do anything that is against the Father's will.
How to get into it
This Marian Consecration may be accompanied by a series of meditations or reflections in preparation, but it is not necessary. All a person needs to do is to be devoted to Mary (pray the rosary every day, go to Mass every day, etc.), to desire to be closer to her, and to renew his/her consecration often through saying a prayer of consecration (such as St. Maximilian Kolbe's Prayer of Total Consecration). Other prayers are certainly available and allowable for use in praying to Mary. (The Litany to Mary, Saint Louis de Montfort's Prayer to Mary)
Choose a date (a good one is one of Mary's many feasts) to consecrate yourself to Mary. The best way to make your initial consecration is in public. (i.e. during Mass) You should renew this consecration on that same day every year.