Although I know what the Church teaches, I have no idea where to go to find out when and where the Church officially defined its teachings. How can I as a layman find out which councils and papal encyclicals taught a given doctrine? I'd be willing to go to the library and do the research but I wouldn't know where to begin, nor even if a public library would carry the types of books I'd need (our parish library has nothing that's helpful). Where can I find such information?
You don't need to spend long hours of drudgery at the library, just a few minutes of drudgery in the comfort of your own home. There are two books that, between them, will furnish you with all the specifics of Church teaching you could ever want. We use them all the time.
The first is The Christian Faith in the Doctrinal Documents of the Catholic Church (Staten Island: Alba House, 1982). Jesuit theologians J. Neuner and J. Dupuis, the editors of this excellent one-volume resource, have catalogued the major doctrines of the Catholic faith according to the official documents of the Church.
The categories include Scripture and Tradition, the Trinity, Christology, justification and salvation, the sacraments (individually treated at length), Marian doctrines, the Mass, ecumenism and the fate of Protestants and other non-Catholics, grace, sexual ethics, the veneration and intercession of the saints, and the use of icons and statues. Relevant passages from the Church Fathers on each subject are cited, as well as pertinent passages from encyclicals and conciliar statements.
The second book you need is Fundamentals of Catholic Dogma, by German theologian Ludwig Ott (Rockford: TAN, 1974). Under each of its sections Fundamentals cites the Bible verses which explicitly and implicitly demonstrate Church doctrine (a handy feature when dealing with Evangelicals and Fundamentalists) It cites the works of the Church Fathers, and it lists the Church councils which dealt with the issue.
Another reason this book is so helpful is that Ott has outlined the arguments against each doctrine, listing the opponents and explaining why their arguments fall flat. Each doctrine is classified according to its degree of certitude--from de fidei definita (such as the Trinity, the Eucharist, and purgatory) down to opinio tolerata, a theological opinion which is merely tolerated by the Church but is in no way binding on the faithful.