The Church offers us different prayers that we can say every day of the week for the faithful departed. These are especially useful for offering a novena on behalf of the dead, or for praying during those seasons of the year (November, in the Western Church; Lent, in the Eastern Church) designated by the Church as times of fervent prayer for the dead.
On Tuesdays, Catholics pray this prayer for the souls of the faithful departed.
Tuesday Prayer for the Faithful Departed
O Lord God omnipotent, I beseech Thee by the Precious Blood of Thy divine Son Jesus that was shed in His bitter crowning with thorns, deliver the souls in purgatory, and among them all, particularly that soul which is in the greatest need of our prayers, in order that it may not long be delayed in praising Thee in Thy glory and blessing Thee for ever. Amen.