Here is a clear and concise statement of the Church's teaching on "Extra Ecclesiam Nulla Salus," taken from none other than Archbishop Marcel Lefebvre. I particularly chose him because many of the people who hold that baptism by implicit desire is a novel concept refer to themselves as "traditionalists," and some even refer to Archbishop Lefebvre as a model of how one should act towards Vatican II.
"We must say it clearly: such a concept is radically opposed to Catholic dogma. The Church is the one ark of salvation, and we must not be afraid to affirm it. You have often heard it said, "Outside the Church there is no salvation"--a dictum which offends contemporary minds. It is easy to believe that this doctrine is no longer in effect, that it has been dropped. It seems excessively severe.
Yet nothing, in fact, has changed; nothing can be changed in this area. Our Lord did not found a number of churches: He founded only One. There is only one Cross by which we can be saved, and that Cross has been given to the Catholic Church. It has not been given to others. To His Church, His mystical bride, Christ has given all graces. No grace in the world, no grace in the history of humanity is distributed except through her.
Does that mean that no Protestant, no Muslim, no Buddhist or animist will be saved? No, it would be a second error to think that. Those who cry for intolerance in interpreting St. Cyprian's formula, “Outside the Church there is no salvation,” also reject the Creed, “I confess one baptism for the remission of sins,” and are insufficiently instructed as to what baptism is. There are three ways of receiving it: the baptism of water; the baptism of blood (that of the martyrs who confessed the faith while still catechumens) and baptism of desire.
Baptism of desire can be explicit. Many times in Africa I heard one of our catechumens say to me, “Father, baptize me straightaway because if I die before you come again, I shall go to hell.” I told him “No, if you have no mortal sin on your conscience and if you desire baptism, then you already have the grace in you.”
The doctrine of the Church also recognizes implicit baptism of desire. This consists in doing the will of God. God knows all men and He knows that amongst Protestants, Muslims, Buddhists and in the whole of humanity there are men of good will. They receive the grace of baptism without knowing it, but in an effective way. In this way they become part of the Church.
The error consists in thinking that they are saved by their religion. They are saved in their religion but not by it. There is no Buddhist church in heaven, no Protestant church. This is perhaps hard to accept, but it is the truth. I did not found the Church, but rather Our Lord the Son of God. As priests we must state the truth."(Archbishop Lefebvre, Open Letter to Confused Catholics)