Here are a few of the topics and ideas you'll find in the second half of Apostolicam Actuositatem.
Chapter IV – The Different Forms of the Apostolate
* Every lay person is obliged to practice the lay apostolate at all times and in all places.
* In the practice of the individual apostolate, the lay person witnesses to Christ with his or her whole life; manifests faith, hope, and charity; proclaims Christ; professes, explains, and spreads His teaching; worships and prays publicly; accepts the difficulties of life in imitation of Christ; and governs his or her behavior by Christian values in all circumstances.
* Through these activities, individual lay people cooperate with God and “contribute to the salvation of the entire world.”
Individual Apostolate in Certain Circumstances
* In places where clergymen are curtailed in the practices of their ministry, lay people take a special role in teaching their fellow Christians and helping to care for souls.
* Where Christians are “few and scattered,” lay people have a special responsibility to exercise their apostolate. They should try to gather as much as possible for mutual support and friendship.
* The opportunities for group apostolate are numerous, and such activities are necessary, for humans are “social by nature.” The group apostolate shows forth the “communion and unity of the Church in Christ.”
* Lay people must practice their aposotolate in “a spirit of concord” as they work in their families, parishes, and dioceses and wherever they form “free associations” among themselves.
* The group apostolate allows for better support, training, and organization for apostolic activities, and can produce a “much richer harvest.”
Various Types of Group Apostolate
* Apostolic organizations for lay people vary greatly according to their goals and methods. Some practice a general apostolate while others focus on specific areas like evangelization, charitable works, or “permeation of the temporal order by the Christian spirit.”
* Organizations that seek to promote unity between Christian faith and everyday life are of great importance.
* International organizations of lay people should be promoted.
* Laity may establish and direct their own organizations as long as they maintain the “necessary link with ecclesiastical authority.”
* Catholic Action refers to a type of lay apostolate that 1. has the goals of evangelization and sanctification of all people, the formation of the Christian conscience, and the spread of the Gospel spirit throughout the world; and 2. is directed by lay people acting in unison under the guidance of the hierarchy.
* Catholic Action is especially commended by the bishops.
* The hierarchy may choose to specially commend lay organizations that meet particular needs.
* Lay people who offer their professional service to the apostolate are to be specially respected and praised.
Chapter V – The Order to Be Observed
* The lay apostolate “must be set in its true place within the apostolate of the whole Church.” Lay people collaborate among themselves and unite with other members of the Church to fully and efficiently practice the aposolate. The hierarchy guides the entire activity.
Relations with the Hierarchy
* The hierarchy recognizes the importance of the lay apostolate, provides it with “principles and spiritual assistance,” directs it for the “common good of the Church,” and ensures that “doctrine and order are safegaurded.”
* All lay organizations must be approved by ecclesiastical authority if they are to claim the name “Catholic.”
* Some lay organizations receive a special mandate to work in close conjunction with apostolic functions of the hierarchy.
* Those lay people who perform some of the duties of pastors are “fully subject to superior ecclesiastical control” in these activities.
* The hierarchy must especially teach and interpret the moral principles and make sure that the lay apostolate is in full conformity with these principles so as to safeguard and promote the “values of the supernatural order.”
Relations with the Clergy and Religious
* The laity plays an important part in the Church's apostolate, and clergy and religious work with the laity as siblings.
* Good relations and constant dialogue between the laity and the clergy are necessary.
* Priests provide lay people with spiritual guidance, wise advice, and encouragement.
* Religious assist both priests and lay people according to the “spirit and rules of their institute.”
* If possible, dioceses should set up special councils to assist the laity in their work and to promote cooperation between clergy and laity.
* The Holy See will have a special secretariat to serve and promote the lay apostolate.
Cooperation with Other Christians and Non-Christians
* Catholics often cooperate with other Christians and even non-Christians especially in charitable activities.
* In such circumstances, lay Catholics must always bear witness to Christ.
Chapter VI – Training for the Apostolate
The Need for Training
* Lay people's training must be “many-sided and complete” if their apostolate is to be effective. Lay people should make “continuous spiritual and doctrinal progress.”
Principles of Training
* Training should be particularly geared to the laity and their place in the secular world.
* Lay education should emphasize the mission of the Church, the life of faith, and the practice of love. Lay people should receive spiritual formation and a “solid grounding in doctrine,” including theology, philosophy, and ethics. Practical and technical training should also be given.
* Education is a continuous process that should guide lay Catholics to live their faith in all areas of their lives and to “enter actively into the service of the Church.”
* This training helps lay people take their places as living witnesses to Christ and the Church in the temporal order.
Those Who Train Others for the Apostolate
* Training should start early in childhood. Parents are the first to prepare children for their apostolate within the family, which is “a kind of apprenticeship to the apostolate.”
* Children should participate early on in their parishes, and schools must foster “a Catholic outlook and apostolic action” in their students.
* Lay associations also assist in the education of their fellow lay people.
* Lay people must take responsibility for their own education as they grow older. They will become more aware of their talents and charisms and learn how to use them best in service to Christ and the Church.
Fields Calling for Specialized Training
* Those taking part in activities of evangelization and sanctification should receive careful formation in Catholic doctrine and learn how to confront materialism in the world.
* Those specially involved in the “Christian renewal of the temporal order” must learn “the true meaning and value of temporal goods” as well as the right uses for those goods. They should be aware of Catholic social teaching and be able to apply its principles in specific cases.
* Those participating in charitable works should learn “how to sympathize with their brothers, and help them generously when in need.”
Aids to Training
* Lay people can take advantage of the many aids to training including books, periodicals, sessions, recollections, congresses, retreats, meetings, and conferences.
* Centers for higher learning and for research should be established.
* The Council exhorts lay people to “give a willing, noble and enthusiastic response to the voice of Christ,” Who calls them to participate in the apostolate of the Church and unite ever more intimately with Him.
* Christ sends the laity into every place throughout the world that they may share in His work.
The full text of Apostolicam Actuositatem is available online at the Vatican website.