If one follows the Usus Antiquior then the eve of Septuagesiama was the day to bury the Alleluia until Easter. In the Novus Ordo it would be either the Sunday before Lent or Shrove Tuesday. Thus, for example, from tomorrow in the Roman Breviary at the end of versicles and responses instead of "Alleluia " "Laus tibi rex aeternae gloriae" is chanted at Solemn Vespers.
The custom was well established by the High Middle Ages as I have outlined in my past posts Burying the Alleluia and in Alleluia dulce carmen - another Neale translation.
There are examples of the practice being revived in places these days - indeed my post last year was followed by an e-mail from Christ Church cathedral here about their plans to do so.
There is are illustrated posts about the ceremony in 2010 in the Church of our Lady of the Atonement in San Antonio in Texas which can be seen here and from 2011 here.
Also in the USA the diocese of Paterson in New Jersey has revived it with a diocesan celebration presided over by the Bishop. There is an article about this from the diocesan website at 'Burying the Alleluia' - Diocese of Paterson, and there is a link to slideshow of the Solemn Vespers, presided over by Bishop Edward Serratelli, at which the interment occurred here.
The funeral procession of Alleluia in Paterson Cathedral