Ordained deacons, priests and bishops can preach.
I’m not aware of laity taking a part in anything other than an announcement about the annual stewardship campaign or some other ministries.
Who is allowed to preach the homily?
The homily, which is given in the course of the celebration of Holy Mass and is a part of the liturgy itself, “should ordinarily be given by the priest celebrant himself. He may entrust it to a concelebrating priest or occasionally, according to circumstances, to a deacon, but never to a layperson. In particular cases and for a just cause, the homily may even be given by a bishop or a priest who is present at the celebration but cannot concelebrate” (64; cf. GIRM 66).At my parish they have a seminarian who is doing his “pastoral year,” and they sometimes have him preach the homily “to practice for what he will have to do later.” Surely that is allowed.
The prohibition of the admission of laypersons to preach within the Mass applies also to seminarians, students of theological disciplines, and those who have assumed the function of those known as “pastoral assistants”; nor is there to be any exception for any other kind of layperson, or group, or community, or association (66).