To my understanding it is not an actual liturgical act, so how it is done varies greatly from place to place and there is no existing ritual to follow.
We have a plaque of the alleluia that I’ve made that our priests carry in procession at the end of mass to a side altar and then cover with a white shroud. We sing ‘Alleluia Song of Gladness’ during this time which I’ve attached and you’re most welcome to use. I took for our model a video I found of Cantius one time.
Alleluia Dulce Carmen • Full score • 2021-01-11.pdf
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