It's too late to do a novena in his honor for his feast day this year, but here's one you can do next year:
O glorious descendant of the kings of Judah, Inheritor of the virtues of all the patriarchs. Just and happy St. Joseph, listen to my prayer. Thou art my glorious protector, and shall ever be, after Jesus and Mary the object of my most profound veneration and confidence. Thou art the most hidden, though the greatest Saint, and art particularly the patron of those who serve God with the greatest purity and fervor. In union with all those who have ever been most devoted to thee I now dedicate myself to thy service; beseeching thee, for the sake of Jesus Christ, who vouchsafed to love and obey thee as a son, to become a father to me; and to obtain for me the filial respect, confidence and love of a child towards thee.
O powerful advocate of all Christians, whose intercession, as St. Theresa assures us, has never been found to fail, deign to intercede for me now, and to implore for me the particular intention of this Novena.
(Mention your intentions here)
Recite one Our Father, one Hail Mary, and one Glory Be.
Present me O great Saint to the adorable Trinity, with Whom thou hadst so glorious and so intimate a correspondence. Obtain that I may never efface by sin the Sacred Image according to the likeness of which, I was created. Beg for me that my divine Redeemer would enkindle in my heart and in all hearts, the fire of His Love, and infuse therein the virtues of His adorable infancy, His purity, simplicity, obedience, and humility.
Obtain for me likewise a lively devotion to thy virgin spouse, and protect me so powerfully in life and death, that I may have the happiness of dying as thou didst, in the friendship of my Creator, and under the immediate protection of the Mother of God. Amen.
It is apparently the custom to begin this prayer on March 10 and end it on the 18th, the eve of his feast.
Shrines of Saint Joseph you can make a pilgrimage to:
More on Saint Joseph
at the OrthodoxWiki
Saint Joseph, pray for us!