Classically, to the Father through the Son in the power of the Holy Spirit. Eucharistic Prayers are thus worded; and the collects in the old Sacramentaries usually do this. Antiphons and hymns, and 'private' prayers such as Veni, Suscipe and Placeat, however, can address the Son, the Spirit, the Trinity, the Saints.
Quite early, however, some confusion arose about which person of the blessed Trinity is being invited to "come" in some of the more 'immediate' Advent collects ("Stir up thy power and come ..."). In the Middle ages and later collects were composed addressing the Son; the most celebrated example of which is the one which was (probably) composed by S Thomas for Corpus Christi. Amusingly, the 1980 Anglican Alternative Service Book primly reconstructed this prayer so that it addressed the Father! But are there collects addressed to the Holy Trinity?
Since 1549, there has been at least one in the Church of England: look at the Trinity Sunday collect as offered by Cranmer. Since 1980, we have had another prayer addressed to the Trinity - now labelled as a postcommunion - which originated in the church of South India. And Cranmer went even further: the Preface for that Sunday was so modified by him that it, too, addresses the Trinity. So here we have (part of) a Eucharistic Prayer addressing not the Father but the Trinity. The latest Church of Ireland Prayer Book goes even further; it has one which addresses the Father in the Preface, the Son in the Institution narrative, the Spirit in the epicletic paragraph, and the Trinity in the Doxology! I have wondered whether such a prayer can even be a valid Form, and have declined to use it.
But I think I have read somewhere that in, for example, the Ethiopian Church, there are Eucharistic Prayers which address the Son and even ... Our Lady!!
Can anyone put me right on this?