We've been practicing this devotion for at least the last 10 years and we always begin on the 20th of February. We like this particular time frame for two reasons:
1. It is a wonderful devotion to do as a family during Lent. We are always guaranteed that at least a portion, if not all, of it will fall during the Lenten season.
2. Beginning on the 20th allows us to make our Consecration on March 25th, the Feast of the Annunciation.
If you aren't familiar with this devotion, here is a website which will give you the basic information, and even the prayers to pray. It isn't too late to grab yourself a book and get started.