Vatican Website translation:

36. 1. Particular law remaining in force, the use of the Latin language is to be preserved in the Latin rites.
2. But since the use of the mother tongue, whether in the Mass, the administration of the sacraments, or other parts of the liturgy, frequently may be of great advantage to the people, the limits of its employment may be extended. This will apply in the first place to the readings and directives, and to some of the prayers and chants, according to the regulations on this matter to be laid down separately in subsequent chapters.
3. These norms being observed, it is for the competent territorial ecclesiastical authority mentioned in Art. 22, 2, to decide whether, and to what extent, the vernacular language is to be used; their decrees are to be approved, that is, confirmed, by the Apostolic See. And, whenever it seems to be called for, this authority is to consult with bishops of neighboring regions which have the same language.
4. Translations from the Latin text into the mother tongue intended for use in the liturgy must be approved by the competent territorial ecclesiastical authority mentioned above.

Latin text:

36. §1. Linguae latinae usus, salvo particulari iure, in Ritibus latinis servetur.
§2. Cum tamen, sive in Missa, sive in Sacramentorum administratione, sive in aliis Liturgiae partibus, haud raro linguae vernaculae usurpatio valde utilis apud populum exsistere possit, amplior locus ipsi tribui valeat, imprimis autem in lectionibus et admonitionibus, in nonnullis orationibus et cantibus, iuxta normas quae de hac re in sequentibus capitibus singillatim statuuntur.
§3. Huiusmodi normis servatis, est competentis auctoritatis ecclesiasticae territorialis, de qua in art. 22 § 2, etiam, si casus ferat, consilio habito cum Episcopis finitimarum regionum eiusdem linguae, de usu et modo linguae vernaculae statuere, actis ab Apostolica Sede probatis seu confirmatis.
§4. Conversio textus latini in linguam vernaculam in Liturgia adhibenda, a competenti auctoritate ecclesiastica territoriali, de qua supra, approbari debet.

Slavishly literal translation:

36. §1. The use of the latin language, particular law excepted, should be preserved in the latin Rites.

§2. Nevertheless since, whether in Mass, or in the administration of the Sacraments, or in other parts of the Liturgy, the use of the vernacular language by no means extraordinarily could appear very useful among the people, a more ample place should be given to it, indeed in first place in the readings and admonitions, in some of the prayers and chants, according to the norms that concerning this topic will be established in the following chapters.

§3. The norms being observed in this fashion, it is of the competent ecclesiastical territorial authority, noted in art. 22 § 2 (also, if the case should arise, having taken the counsel of the Bishops of the surrounding regions of the same language) to establish the use and manner/style of the vernacular language, with these acts tested/approved or confirmed by the Apostolic See.

§4. The translation of latin texts into the vernacular language for use in the Liturgy ought to be approved by the competent ecclesiastical territorial authority, as noted above.

The last of the norms based on the pastoral and teaching character of the Liturgy enacted by the Council Fathers concern the use of the vernacular in Catholic worship.

The Fathers decree that the use of Latin in the Latin rites is to be maintained, but they do not indicate (at least in this place) to what extent and how the decree is to be implemented. Some have suggested that art. 36.1 displays some tension with art. 34’s call for rites “accommodated to the capacity/grasp of the faithful” and the repeated calls for “full, conscious, and active participation” of the faithful in liturgical worship.

The Fathers further decree that the use of vernacular languages in liturgical worship may certainly occur in the (scriptural) readings and presidential directives, as well as in certain prayers and chants. They do not limit the use of the vernacular to these categories, but make it clear that these categories would be the first areas in which vernacular translations would be made.

The Fathers go on to decree that local territorial authorities are to judge if and to what extent this permission for the use of vernacular language in liturgical worship is to apply to their local churches. Most interestingly, in the light of recent controversies about the English translation of the Roman Missal, art. 35.4 squarely places the responsibility for vernacular liturgical translations on local territorial authorities, although one might assume that the oversight of the Apostolic See mentioned in art. 35.3 would apply here as well.