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.
Catholics pray this prayer on Wednesdays for the souls of the faithful departed.
Wednesday 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 the streets of Jerusalem whilst He carried on His sacred shoulders the heavy burden of the Cross, deliver the souls in purgatory and especially that one which is richest in merits in Thy sight, so that, having soon attained the high place in glory to which it is destined, it may praise Thee triumphantly and bless Thee for ever. Amen.