What does it mean for a person to be consecrated to St. Joseph? Well, it basically means that you acknowledge that he is your spiritual father, and you want to be like him. To show it, you entrust yourself entirely into his paternal care so that he can help you acquire his virtues and become holy. Total consecration to St. Joseph means you make a formal act of filial entrustment to your spiritual father so that he can take care of your spiritual well-being and lead you to God. The person who consecrates himself to St. Joseph wants to be as close to their spiritual father as possible, to the point of resembling him in virtue and holiness. Saint Joseph, in turn, will give those consecrated to him his undivided attention, protection, and guidance.
The consecration is a 33 day retreat and you meet once a week to talk about what you've read and discuss the challenges and knowledge that you've gained.
More information can be found here.
St. Joseph Consecration