4.2.2 Preaching by the Lay Faithful
1. Only a Catholic priest or deacon may preach at the time reserved for the homily at a Catholic Eucharistic liturgy. 
2. The non-ordained faithful may preach at liturgy other than the Eucharist only when expressly permitted by law and when its prescriptions are observed.  (See #188.8.131.52 Authorizations of those Entrusted with Participation in the Pastoral Care of Parishes.)
3. In the absence of a cleric or his inability to preach for some reason, a lay Catholic may be authorized to preach by the pastor or rector in a church or oratory but only in these circumstances outside the celebration of the Eucharist:
a. a celebration of the Liturgy of the Hours;
b. a penitential service (a non-sacramental event; see #5.4.4 Penitential Services);
c. any of the rites of Christian funeral (i.e., a vigil or committal, and at a funeral home or cemetery);
d. a "communion service" or a "Sunday Celebration in the Absence of a Priest" (see #5.3.4 Communion Services and Sunday Celebrations in the Absence of a Priest).
e. Such authorization cannot be given for the celebration of Baptism, marriage, the Anointing of the Sick or Penance, even though celebrated outside of the Mass.
4. However, “a form of instruction designed to promote a greater understanding of the liturgy, including personal testimonies, or the celebration of Eucharistic liturgies on special occasions (e.g. day of the Seminary, day of the sick etc.) is lawful, in harmony with liturgical norms, should such be considered objectively opportune as a means of explicating the regular homily preached by the celebrant priest. Nonetheless, these testimonies or explanations may not be such so as to assume a character which could be confused with the homily.”  It is usually best to have these done after the communion prayer.
 c. 767§1; PCAI May 1987; Collaboration, art. 3; RS, nn. 65-66; USCCB c. 766. Pontifical Council for Promoting Christian Unity, Directory for the Application of Principles and Norms on Ecumenism Directoire pour L'application des Principes et des Normes sur L'oecuménisme; Directorium oecumenicum noviter compositum (March 25, 1993) n. 134 in AAS 85  pp. 1039-1119. Available at the Vatican website.
 cc. 762-772; USCCB c. 766; Collaboration, art. 3 § 4.
 Collaboration, art. 3 § 2.