On 31 December the faithful can gain a Plenary Indulgence by public recitation or singing of the Te Deum.
On 1 January the faithful can gain a Plenary Indulgence by public recitation or singing of the Veni Creator.
From the Enchiridion Indulgentiarum (2004 – my emphases):
26 §1. Plenaria indulgentia conceditur christifideli qui, in ecclesia vel oratorio, devote interfuit sollemni canuti vel recitationi:
1º hymni Veni, Creator, vel prima anni die ad divinam opem pro totius anni decursu implorandam, vel in sollemnitate Pentecostes;
2º hymni Te Deum, ultima anni die, ad gratias Deo referendas pro benefixiis totius anni decursu acceptis.
You must do the work in the state of grace, make a sacramental confession within 20 days of the work, pray for the Pope’s intentions, and have no attachment to sin, even venial sin. It is sufficient to make a sincere act of will to love God and despise all sin.
The Pope’s intentions for December 2008 (for today and the Te Deum) are:
That in the face of a spreading of a culture of violence and death the Church through her apostolic and missionary activity may promote with courage the culture of life.
That especially in mission countries Christians may show with acts of fraternal love that the Child born in the stable at Bethlehem is the luminous Hope of the world.
The Holy Father’s intentions for January 2009 (and the Veni Creator indulgence) are:
…yet to come… I haven’t found them yet.