For the Akathist to Saint Joseph, visit the website of the Antiochian Men, whose patron is Saint Joseph. They broadcast the Akathist, which they offer every year on December 26.
For prayers to Saint Joseph, on this Feast or offered for 9 days, the text (adapted from the Akathist) is:
O holy, righteous Joseph!
While still living on earth, you had great boldness before the Son of God, who was pleased to call you His father, as you were betrothed to His Mother, and to obey you:
we believe that now, having taken up your abode with the choirs of the righteous in heavenly habitations, you will be heard in your petitions to our God and Savior.
Therefore, taking refuge in your protection and help, we ask and humbly entreat you that as you yourself were delivered from the storm of doubtful thoughts, so too deliver us who are beset by the stormy waves of our troubles and worries; as you did protect the all-pure Virgin from human slander, guard us likewise by your holy prayers; as you did keep the incarnate Lord from all harm and evil intent, keep also His Holy Church and all of us unworthy servants from all malice and harm.
You know, O Saint of God, that the Son of God too, in the days of His incarnation, had need of bodily things, and you did serve Him humbly; for this cause, we ask for your prayers: help us in our needs of soul and body by your intercession, and especially we ask you to pray Him Who was called your son, Who is the Only-begotten Son of God, our Lord Jesus Christ, to grant us remission of our sins, [add special intentions here],
May we be worthy of inheritance in the kingdom of heaven, so that, taking up our abode in the higher habitations with thee, we may always glorify the God Who is One in the Holy Trinity: the Father, and the Son, and the Holy Spirit, now and unto ages of ages. Amen.