Pr David Petersen reproduces a piece from Pius Parsch concerning the disappearance of the word "Alleluia" in the Western liturgy during Septuagesima Season, Lent and Passiontide. And Pr William Weedon reproduces a wonderful meditation by O. P. Kretzmann on this uniquely Western Christian practice. Using rationale similiar to the Eastern churches, Luther questioned this practice of dispensing with the Alleluia, but Lutherans have maintained it nevertheless.
Parsch mentions that "considerable ceremony" accompanies the dispensing of the Alleulia in some places. While no ceremony is indicated in the latest Liber Usualis, the Tridentine Secular Breviary, or the Monastic Diurnal, the Anglican Breviary indicates that on "Alleluia Saturday" (the day before Septuagesima Sunday) an 11th century hymn entitled "Alleluia, dulce carmen" is to be sung. (Go here or here for an Enlgish translation.)
I commend this hymn to you for your devotion.
All the breviaries mentioned above, however, agree that in the closing versicles the following is said: "Let us bless the Lord, alleluia, alleluia." Then they add: "Henceforth Alleluia is not said until Holy Saturday [at the Great Vigil of Easter]."
What happens then at those places in the Mass and Divine Office when Alleluia is usually sung? At the Mass, the "Alleluia" (following the Gradual) is replaced with the Tract. At the Divine Office, in the opening versicles the "Alleluia" is replaced with "Praise be to Thee, O Lord, King of eternal glory."