From the General Instruction of the Roman Missal:
69. In the Universal Prayer or Prayer of the Faithful, the people respond in some sense to the Word of God which they have received in faith and, exercising the office of their baptismal Priesthood, offer prayers to God for the salvation of all. It is desirable that there usually be such a form of prayer in Masses celebrated with the people, so that petitions may be offered for holy Church, for those who govern with authority over us, for those weighed down by various needs, for all humanity, and for the salvation of the whole world.
70. The series of intentions is usually to be:
a) for the needs of the Church;
b) for public authorities and the salvation of the whole world;
c) for those burdened by any kind of difficulty;
d) for the local community.
Nevertheless, in any particular celebration, such as a Confirmation, a Marriage, or at a Funeral, the series of intentions may be concerned more closely with the particular occasion.
71. It is for the Priest Celebrant to regulate this prayer from the chair. He himself begins it with a brief introduction, by which he calls upon the faithful to pray, and likewise he concludes it with an oration. The intentions announced should be sober, be composed with a wise liberty and in few words, and they should be expressive of the prayer of the entire community.
They are announced from the ambo or from another suitable place, by the Deacon or by a cantor, a reader, or one of the lay faithful.
The people, for their part, stand and give expression to their prayer either by an invocation said in common after each intention or by praying in silence.